Temsirolimus and Bevacizumab in Treating Patients With Advanced Endometrial, Ovarian, Liver, Carcinoid, or Islet Cell Cancer

Inclusion Criteria: * Histologically or cytologically confirmed endometrial (endometrioid, uterine, papillary serous carcinoma, and carcinosarcoma), ovarian (primary peritoneal/fallopian tube, serous, endometrioid, mixed, and poorly differentiated epithelial ovarian cancers \[for purposes of eligibility, carcinosarcoma is considered a poorly differentiated carcinoma\]), hepatocellular carcinoma, carcinoid or islet cell (neuroendocrine: well- or moderately-differentiated neuroendocrine) cancer which are locally advanced, recurrent, or metastatic * Patients must have measurable disease; patients having only lesions measuring \>= 1 cm to \< 2 cm must use spiral computed tomography (CT) imaging for both pre- and post-treatment tumor assessments; patients who have had prior palliative radiotherapy to metastatic lesion(s) must have at least one measurable lesion(s) that have not been previously irradiated * Radiation therapy (adjuvant or palliative) must be completed \>= 4 weeks prior to registration, if applicable * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelets \>= 75,000/mm\^3 * Hemoglobin \>= 9.0 g/dL * Total bilirubin =\< 1.5 x upper limit of normal (ULN); Note: direct bilirubin and international normalized ratio (INR) for hepatocellular carcinoma (HCC) patients allowed as per Child-Turcotte-Pugh scoring * Alkaline phosphatase =\< 2.5 x ULN (=\< 5 x ULN if liver metastasis is present or patient is in HCC cohort) * Serum glutamic oxaloacetic transaminase (SGOT) (as…