Temsirolimus and Vorinostat in Treating Patients With Metastatic Prostate Cancer

Inclusion * Patients must have a histologically confirmed diagnosis of adenocarcinoma of the prostate that is hormone refractory and with evidence of progressive metastatic disease following docetaxel treatment by any of the following: * Increased serum prostate-specific antigen (PSA) levels confirmed by 3 consecutive PSA measurements (at least 2 weeks apart), the first sample to be taken at least 6 weeks after bicalutamide or megestrol acetate withdrawal AND/OR * Progression of bidimensionally measurable soft tissue (nodal) metastasis by CT scan or MRI within the past 4 weeks AND/OR * Progression of bone disease by at least two new bone lesions on bone scan confirmed by a second bone scan * Patients should be without persisting \>= grade 2 hematological/non-hematological toxicities from previous treatments that would preclude evaluation of toxic effects of study treatment.Grade 1 residual toxicity will be acceptable. Patients should be off prior therapies at least 4 weeks before starting study treatment * Prior palliative radiation to metastatic lesion(s) is permitted, provided there is at least one measurable and/or evaluable lesion(s) that has not been radiated * Castrate levels of serum testosterone (=\< 50 ng/dL or 1.0 mmol/L) confirmed within two weeks prior to Day 1 of treatment. Testosterone levels will not be required for patients who have had bilateral orchiectomy * ECOG performance status 0-1 * Life expectancy of greater than 6 months * Absolute neutrophil count \>= 1,500/mm\^3 * Platelets \>= 100,000/mm\^3 * Hgb \>= 9g/L * Total bilirubin =\< 1.5 x laboratory upper limit of normal (ULN) * AST(SGOT)/ALT(SGPT) \<= 2.5 x laboratory ULN * Creatinine =\< 1.5 x laboratory ULN or calculated creatinine clearance \>= 50 ml/min * Serum amylase =\< ULN (If \> ULN, confirm pancreatic amylase \< 1.1 ukat/L and serum lipase \< ULN) * PT/INR \<= 1.5 * Urine protein \< 1+ or if \>= 1 then 24-hour urine protein should be obtained and should be \< 1000 mg * Serum cholesterol \< ULN with or without treatment for hyperlipidemia; if \> ULN and untreated, may be rescreened for eligibility after treatment * Eligibility of patients receiving any medications or substances known to affect or with the potential to affect the activity or pharmacokinetics of temsirolimus will be determined following review of their case by the Principal Investigator * Patients, if sexually active, will agree to use adequate contraceptive methods (barrier contraceptive with spermicide, vasectomy, abstinence) prior to study entry and for the duration of study participation * Ability to understand and the willingness to sign a written informed consent document * No evidence (\>= 5 years) of prior malignancies except successfully treated basal cell or squamous cell carcinoma of the skin Exclusion * Prior use of HDAC or mTOR inhibitors * Patients with known brain metastases * Any medical condition, including the presence of laboratory abnormalities, which confounds the ability to interpret data from the study or places the patient at unacceptable risk if he participates in the study * History of allergic reactions attributed to compounds of similar chemical or biologic composition to vorinostat or temsirolimus * Concurrent use of other anticancer agents or treatments except LHRH antagonists * Uncontrolled intercurrent illness including, but not limited to the following:(a)Ongoing or active infection including viral hepatitis,(b)Symptomatic congestive heart failure (New York Association Class II, III, or IV),(c) unstable angina pectoris requiring nitrate therapy,(d) prior myocardial infarction,(e)severe uncontrolled ventricular cardiac arrhythmias,(f) uncontrolled hypertension (defined as blood pressure of \> 160 mmHg systolic and/or \> 90 mmHg diastolic on medication),(g)electrocardiographic evidence of acute ischemia(h)Psychiatric illness/social situations that would limit compliance with study requirements * Known positive serology for HIV and known history of HIV because of the potential for pharmacokinetic unforeseen toxicity and morbidity in an immunocompromised patient * Any treatment modalities, including radiation and surgery, not discontinued at least 4 weeks prior to treatment in this study * Chronic Hepatitis with advanced, decompensated hepatic disease or cirrhosis of the liver or history of chronic virus hepatitis or known viral hepatitis carrier (patient recovered from Hepatitis A will be allowed to enter the study) * Simultaneous participation in any other study involving investigational drugs or having participated in a study less than 4 weeks prior to treatment in this study * No investigational or commercial agents or therapies other than those described in the study may be administered with the intent to treat the patient's malignancy