Temsirolimus and Bevacizumab in Treating Patients With Stage III or Stage IV Malignant Melanoma

Inclusion Criteria: * Histologically or cytologically confirmed melanoma * Stage III or IV disease * Recurrent disease allowed * Measurable disease defined as ≥ 1 lesion that can be accurately measured in ≥ 1 dimension as ≥ 20 mm with conventional techniques OR ≥ 10 mm with spiral CT scan * Tumor lesions in previously irradiated areas are not considered measurable disease * Prior brain metastases allowed provided all of the following criteria are met: * No more than a total of 5 brain metastases * All metastases are no more than 2.5 cm * Surgically resected or have been treated with gamma-knife or stereotactic radiosurgery * More than 30 days since prior disease progression * More than 30 days since prior steroids for managing brain metastases * Concurrent steroids for other reasons allowed provided the dose is \< that required for managing brain metastases * Disease accessible for core needle biopsy, incisional biopsy, and/or surgical resection and meets one of the following criteria: * One large tumor deposit ≥ 5 cm³ from which biopsies can be harvested multiple times * Multiple deposits that can be biopsied or excised individually on different dates, measured as follows: * One lesion ≥ 5 cm\^3 * Two lesions ≥ 3 cm\^3 * Three lesions ≥ 2 cm\^3 * ECOG performance status 0-1 * Weight ≥ 110 pounds (without clothes) * WBC ≥ 3,000 mm³ * Absolute neutrophil count ≥ 1,500/mm³ * Platelet count ≥ 100,000/mm³ * Bilirubin normal * AST and ALT ≤ 2.5 times upper limit of normal * Creatinine normal OR creatinine clearance ≥ 60 mL/min * Urine protein: creatinine ratio \< 1.0 OR 24-hour urine protein \< 1,000 mg * Fasting cholesterol \< 350 mg/dL (cholesterol medications are allowed) * Fasting triglycerides \< 400 mg/dL * PT INR ≤ 1.5 (unless on full-dose anticoagulants) * Hematocrit \< 41% (for males) or \< 38% (for females) * None of the following within the past 4 weeks: * Uncontrolled intercurrent illness * Ongoing or active acute (CTCAE v.3 grade 3 or 4) infection * Abdominal fistula * Gastrointestinal perforation * Intra-abdominal abscess * Serious or nonhealing wound, ulcer, or bone fracture * No psychiatric illness or social situations that would preclude study compliance * No clinically significant cardiovascular disease, including the following: * Cerebrovascular accident within the past 6 months * Transient ischemic attack within the past 6 months * Myocardial ischemia within the past 6 months * Myocardial infarction within the past 6 months * Other thromboembolic event within the past 6 months * Unstable angina within the past 6 months * Uncontrolled hypertension (i.e., hypertension despite maximal therapy) * New York Heart Association class II-IV heart disease * Congestive heart failure * Serious cardiac arrhythmia requiring medication * Clinically significant peripheral vascular disease * History of stroke * Artificial valve, pacemaker, or similar device * No uncontrolled diabetes * Hemoglobin A1c \< 7% * No significant traumatic injury within the past 28 days * No history of allergic reactions to compounds of similar chemical or biological composition to temsirolimus or bevacizumab * No hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies (e.g., infliximab) * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for ≥ 6 months after completion of study treatment * HIV negative * Hepatitis C negative * See Disease Characteristics * More than 4 weeks since any of the following prior treatments and recovered: * Chemotherapy (6 weeks for nitrosoureas or mitomycin C) * Radiotherapy to nontarget lesions or lesions that are not to be biopsied * Immunotherapy * Cytokine therapy * Enzyme-inducing antiepileptic drugs (EIAEDs) or other CYP3A4 inducers * Investigational agents * More than 4 weeks since prior major surgery or open biopsy and recovered * No prior temsirolimus, rapamycin, bevacizumab, or systemic therapies targeted primarily to vascular endothelial growth factor (VEGF), VEGF receptors, or to mTOR inhibition * Concurrent full-dose anticoagulants (e.g., warfarin/low molecular weight heparin) with PT INR \> 1.5 are allowed provided the following criteria are met: * In-range INR (usually between 2 and 3.5) on a stable dose of oral anticoagulant or on a stable dose of low molecular weight heparin * No active, clinically significant bleeding or pathological condition that carries a high risk of bleeding (e.g., tumor involving major vessels or known varices) * Minimal tumor bleeding of the skin allowed at the clinician's discretion * No concurrent medications or substances known to affect or with the potential to affect the activity or pharmacokinetics of the following: * Temsirolimus * Bevacizumab * CYP450 isoenzymes * No concurrent nonstudy-related surgical procedures * No other concurrent anticancer agents or therapies Exclusion Criteria * Participants who have received these medications or treatments at any time ≤ 4 weeks of registration: * Chemotherapy * Radiotherapy to non-target lesions and lesions that are not to be biopsied. Prior radiotherapy to target lesions or lesions to be biopsied/resected is not permitted * Immunotherapy * Cytokine therapy * Investigational reagents * Invasive procedures defined as follows: * Major surgical procedure, open biopsy or significant traumatic injury * Anticipation of need for non-study related surgical procedures from registration until Cycle 26 (One year). * Enzyme-inducing antiepileptic drugs (EIAEDs) or any other CYP3A4 inducer (Appendix C). OR Participants who have not recovered from adverse events resulting from the administration of these agents/procedures \> 4 weeks prior to registration. * Participants who have received nitrosureas or mitomycin C ≤ 6 weeks of registration. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to CCI-779 or bevacizumab, or with known hypersensitivity to Chinese hamster ovary cell products (t-PA) or other recombinant human antibodies (e.g., Remicade®). * Participants who have previously received CCI-779, rapamycin, bevacizumab, or systemic therapies targeted primarily to VEGF, VEGF receptors, or to mTOR inhibition. * Participants who have experienced any of the following ≤ 4 weeks prior to registration: * Uncontrolled intercurrent illness * Infection, CTCAE3 grade 3 or 4 (either ongoing, chronic, or active infection) * Abdominal fistula * Gastrointestinal perforation * Intra-abdominal abscess * Serious or non-healing wound * Serious or non-healing ulcer * Serious or non-healing bone fracture. * Potential subjects with clinically significant cardiovascular disease * Recent history (defined as ≤ 6 months of registration) of thromboembolic events including cerebrovascular accident (CVA), transient ischemic attack (TIA), myocardial ischemia, myocardial infarction (MI) * Uncontrolled hypertension (hypertension despite maximal therapy) * Unstable angina ≤ 6 months of registration * New York Heart Association Classification of ≥ class II heart disease * Congestive heart failure * Serious cardiac arrhythmia requiring medication * Clinically significant peripheral vascular disease * Have a history of stroke * Have an artificial valve, pace-maker, or similar device * Psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant (positive pregnancy test) or nursing women. Both fertile men and women must agree to use adequate contraceptive measures during study therapy and for at least 6 months after the completion of their participation in the study therapy. * PT INR \> 1.5, (unless the potential subject is on full dose anticoagulants and meet criteria described in Section 3.1.8). * Participants with uncontrolled diabetes, defined as having a HGBA1C ≥ 7%.