Phase II Combination of Temsirolimus and Sorafenib in Advanced Hepatocellular Carcinoma

INCLUSION CRITERIA 1. Patients must have histologically diagnosed American Joint Committee on Cancer (AJCC) stage II, III, or IV hepatocellular carcinoma (HCC) not eligible for curative resection, transplantation, or ablative therapies 2. Radiographically measurable disease by RECIST version 1.1 in at least one site not previously treated with chemoembolization, radioembolization, or other local ablative procedures (i.e. must have at least one measurable target lesion, either within the liver or in a measurable metastatic site); a new area of tumor progression within or adjacent to a previously-treated lesion, if clearly measurable by a Radiologist, is acceptable 3. No prior systemic cytotoxic chemotherapy or targeted therapy (including sorafenib) for HCC 4. Prior chemoembolization, local ablative therapies, or hepatic resection permitted if completed ≥ 4 weeks prior to study enrollment if patient has recovered with ≤ grade 1 toxicity and if measurable disease (criterion 2) is present 5. Prior radiation for bone or brain metastases is permitted if patient is now asymptomatic and has completed all radiation and steroid therapy (if applicable) for brain or bone metastases ≥ 2 weeks prior to study enrollment. 6. Age ≥ 18 years. 7. Child-Pugh score of A or B with ≤ 7 points and meeting laboratory eligibility for all parameters 8. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 9. Life expectancy greater than 3 months 10. Treatment with appropriate antiviral therapy for patients with active hepatitis B Virus (HBV) infection is required 11. Treatment for clinically-significant hyperglycemia, hyperlipidemia, or hypertension that develops on study is required 12. Baseline blood pressure must be adequately controlled with or without antihypertensive medications prior to enrollment (systolic ≤ 150 mm Hg, diastolic ≤ 90 mm Hg) 13. Baseline cholesterol must be \< 350 mg/dL and triglycerides \< 300 mg/dL (with or without the use of antihyperlipidemic medications) 14. Baseline fasting blood glucose must be ≤ 140 mg/dL and hemoglobin A1c less than 7.5% (with or without the use of anti-diabetic medications) 15. Adequate baseline organ and marrow function as defined below Adequate bone marrow function: absolute neutrophil count \> = 1,000/microliter (mcL) platelets ≥ 75,000/mcL hemoglobin ≥ 8.5 g/dL Adequate hepatic function: total bilirubin ≤ 2 mg/dL or ≤ 1.5 times ULN aspartate aminotransferase (AST) / serum glutamic-oxaloacetic transaminase (SGOT) \& alanine aminotransferase (ALT) / serum glutamic-pyruvic transaminase (SGPT) ≤ 5 X upper limit of normal (ULN) International Normalized Ratio (INR) \<=1. 5 X ULN Adequate renal function: albumin ≥ 2.8 g/dL creatinine ≤1. 5 X ULN 16. Able to tolerate oral therapy. 17. Ability to understand and willingness to provide informed consent, and the willingness to comply with the requirements of the protocol. Informed consent may be obtained with the assistance of a medical translator according to institutional policies. 18. The effects of temsirolimus on the developing human fetus are unknown. For this reason and because sorafenib - also being used in this trial - is known to be teratogenic, women of child-bearing potential must have a negative pregnancy test within 14 days of study enrollment. Also, women of child-bearing potential and men must agree to use two methods adequate contraception (hormonal plus barrier or two forms of barrier) or abstinence prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she needs to inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, or be surgically sterile, for the duration of study participation, and for 3 months after completion of study drug administration. 19. Eligibility of patients receiving any medications or substances known to affect or with potential to affect the activity or pharmacokinetics of temsirolimus and/or sorafenib will be determined following review of the case by the Study Chair. Efforts should be made to switch patients who are taking enzyme-inducing anti-convulsant agents to other medications. 20. mixed histology (mixed HCC-cholangiocarcinoma) tumors if deemed appropriate for HCC therapy by treating MD EXCLUSION CRITERIA: 1. Mixed tumor histology or fibrolamellar variant tumors are excluded. 2. Prior systemic or antiangiogenic therapy for HCC (including thalidomide, sorafenib, sunitinib, or bevacizumab). Prior systemic therapy for other diagnoses is permitted if greater than 6 months have elapsed since last dose, any prior toxicity has recovered to ≤ grade 1 by CTCAE v4.0, and treatment was not discontinued for toxicity. 3. Prior treatment with mTOR inhibitor or other molecularly targeted therapy. 4. Prior systemic cytotoxic therapies for HCC (chemoembolization is permitted if inclusion criteria are met). 5. Treatment with other investigational agents. 6. Immunosuppressive medications including systemic corticosteroids unless used for adrenal replacement, appetite stimulation, acute therapy for asthma or bronchitis exacerbation (≤ 2 weeks), or antiemesis 7. Patients with known HIV infection are ineligible due to risk of pharmacokinetic interactions between anti-retroviral therapy and the study drugs, as well as potential for significant immunosuppression and serious infections with mTOR inhibition. 8. Patients who have undergone liver transplantation are excluded. 9. Uncontrolled hypertension (\> 150/90 mmHg). 10. Uncontrolled hyperlipidemia (total cholesterol \> 350 or triglycerides \> 300). 11. Symptomatic brain or bone metastases; prior radiation and/or steroid therapy for brain or bone metastases (if applicable) must be completed ≥ 2 weeks prior to study enrollment. 12. History of seizure disorder requiring antiepileptic medication or brain metastases with seizures. 13. Serious non-healing wound, ulcer, bone fracture, or abscess. 14. Major surgical procedure less than 4 weeks from start of protocol treatment. 15. Patients requiring chronic anticoagulation with warfarin are excluded. Patients treated with low molecular weight heparin or unfractionated heparin are eligible if on a stable dose without evidence of clinically significant bleeding for at least 2 weeks prior to enrollment. 16. Active second malignancy other than non-melanoma skin cancer or cervical carcinoma in situ. (Patients with history of malignancy are not considered to have a "currently active" malignancy if they have completed therapy and are now considered by their physician to be at less than 30% risk for relapse.) 17. Uncontrolled intercurrent illness including, but not limited to: Ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, uncontrolled cardiac arrhythmia, uncontrolled peripheral vascular disease, myocardial infarction within preceding 12 months, cerebrovascular accident within preceding 12 months, pulmonary disease impairing functional status or requiring oxygen, impairment in gastrointestinal function that may affect or alter absorption of oral medications (such as malabsorption or history of gastrectomy or bowel resection). 18. Patients will be excluded if there is any history of allergic reaction(s) attributed to compounds of similar composition to temsirolimus, sorafenib, their metabolites, or any component of their formulation (including excipients and polysorbate 80). This includes hypersensitivity to macrolide antibiotics due to potential for cross-reactivity with temsirolimus. 19. Pregnant or lactating women are excluded from this study because temsirolimus and sorafenib are drugs with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with temsirolimus or sorafenib, breastfeeding should be discontinued if the mother is receiving temsirolimus/sorafenib treatment. 20. Patients who require prohibited medications with potential for serious interactions with protocol therapy, and who cannot have therapeutic substitution are excluded. Patients receiving any medications or substances that are inhibitors or inducers of CYP450 enzyme(s) are ineligible. Lists of prohibited medications and substances known, or with the potential to interact with the specified CYP450 enzyme(s) isoenzymes are provided in Appendices 6-9 Prohibited Medications 21. Psychiatric illness, other significant medical illness, or social situation which, in the investigator's opinion, would limit compliance or ability to comply with study requirements.