Sorafenib and Temsirolimus in Treating Patients With Metastatic, Recurrent, or Unresectable Melanoma

Inclusion Criteria:

* Histologically or cytologically confirmed melanoma, meeting 1 of the following criteria: recurrent or unresectable stage III disease, stage IV disease, non-choroidal origin.
* Tumor must be accessible to biopsy unless appropriate tumor sample collection has occurred within the past 3 months and patient agrees to provide these samples for this study.
* Eastern Cooperative Oncology Group (ECOG) performance status 0-1.
* Bilirubin normal
* Creatinine normal or creatinine clearance ≥ 60 mL/min
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception during and for 30 days after completion of study treatment.
* No history of allergic reactions attributed to compounds of similar chemical or biological composition to sorafenib or temsirolimus.
* No uncontrolled hypertension, defined as systolic blood pressure \> 140 mm Hg on 2 separate days \< 1 week prior to study entry OR diastolic pressure \> 90 mm Hg on 2 separate days \< 1 week prior to study entry.
* No evidence of bleeding diathesis or coagulopathy.
* No condition that would impair the ability to swallow pills (e.g., gastrointestinal tract disease resulting in an inability to take oral medication; requirement for IV alimentation; or active peptic ulcer disease).
* No uncontrolled illness including, but not limited to, any of the following: ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia or psychiatric illness or social situations that would limit study compliance.
* No traumatic injury within the past 3 weeks.
* No more than 1 prior systemic chemotherapy regimen for metastatic melanoma (Phase II).
* No prior sorafenib, temsirolimus, or any other agents targeting raf, vascular endothelial growth factor (VEGF)/VEGF receptor, or mTOR (Phase II).
* No prior surgical procedures affecting absorption.
* At least 3 weeks since prior major surgery.
* At least 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin C) for melanoma and recovered.
* At least 4 weeks since prior radiotherapy and recovered.
* Prior biologic or immunotherapeutic regimens allowed.
* Prior regional chemotherapy regimens (e.g., isolated limb perfusion) allowed but only 1 prior regional chemotherapy regimen allowed if all target lesions are within the prior regional treatment field.
* No concurrent enzyme-inducing antiepileptic drugs including, but not limited to, any of the following: phenytoin, carbamazepine, phenobarbital, rifampin or Hypericum perforatum (St. John's wort).
* No concurrent prophylactic hematopoietic colony-stimulating factors.
* No other concurrent investigational agents.
* No other concurrent anticancer agents or therapies for this cancer.
* No concurrent full-dose anticoagulation (i.e., warfarin, IV heparin, or low-molecular weight heparin).
* No concurrent grapefruit or grapefruit juice.
* No concurrent combination antiretroviral therapy for HIV-positive patients.
* Concurrent prophylactic anticoagulation therapy (e.g., low-dose warfarin) allowed provided prothrombin time (PT) international normalized ratio (INR) \< 1.1 times upper limits of normal (ULN).
* Unidimensionally measurable disease \>= 20 mm by conventional techniques or \>= 10 mm by spiral computed tomography (CT) scan (longest diameter to be recorded) and margins of visible cutaneous metastatic lesions should be clearly defined and measured in at least one dimension as \>= 10 mm.
* No known brain metastases unless the following criteria are met: no radiographical evidence of recurrences in the brain \>= 3 months after complete resection of the brain metastases, asymptomatic brain metastases stable for \>= 3 months since whole-brain radiation therapy and/or stereotactic radiosurgery and must not require steroid for brain metastases.
* White Blood Count (WBC) \>= 3,000/mm³
* Absolute neutrophil count \>= 1,500/mm³
* Platelet count \>= 100,000/mm³
* Serum cholesterol =\< 350 mg/dL
* Triglycerides =\< 400 mg/dL
* Alanine aminotransferase (ALT)/aspartate aminotransferase (AST) =\< 2.5 times upper limit of normal.
* No peripheral neuropathy \> grade 2.
* At least 5 years since prior chemotherapy for other types of cancer.