The purpose of this research study is to determine the safety of the combination of the two drugs cediranib and temsirolimus and the highest doses of these two drugs that can be given in combination to people safely. Cediranib is a drug that may stop blood supply to the tumor and therefore help keep cancer cells from growing. Temsirolimus is a drug that may stop cancer cells from growing. These drugs have been used in other research studies in ovarian and kidney cancer and these studies suggest that these drugs may help to keep cancer from growing in this research study.

• We are looking for the highest dose of the study drugs that can be administered safely without severe or unmanageable side effects in participants that have recurrent gynecological cancers. Not everyone who participates in this research study will receive the same dose of the study drug.
• There will be samples of blood taken that measure any additional effect of the study drugs and to look for a marker for the participant's particular type of cancer. Blood will be taken at a certain point in the study to evaluate the interaction of the two study drugs, cediranib and temsirolimus when given together. These are called pharmacokinetic (PK) samples. About 6 teaspoons of blood will be taken with each PK sample with a total of 34 samples taken.
• Participants will be given a study medication diary for each treatment cycle. Each cycle lasts four weeks (28 days). Temsirolimus will be given on days 1, 8, 15 and 22 of each cycle. Cediranib wil be taken orally once daily in the morning.
• Participants will be asked to monitor their blood pressure on a daily basis at home and keep a blood pressure diary.
• The following tests and procedures will be performed at specific time periods during the course of the study: medical history; side effect assessment; physical exam; vital signs; blood tests; CT scan; MUGA or ECHO; EKG and urine test.

Inclusion Criteria:

• Patients with metastatic endometrial cancer
• Patients with recurrent ovarian, fallopian and peritoneal cancer
• Patients with recurrent cervical cancer
• Patients may have either measurable or non-measurable disease
• Up to one prior line of chemotherapy in the recurrent setting is allowed. Biologic therapies will be considered as a prior line but hormonal therapies do not count.
• No prior VEGF inhibitor therapy allowed.
• Toxic side effects related to prior chemotherapy or hormonal therapy must have resolved to less than or equal to grade 1 or to baseline (excluding alopecia), or for peripheral neuropathy to less than or equal to grade 2.
• Subjects may begin AZD2171 and temsirolimus at least 3 weeks after their last dose of chemotherapy or hormonal therapy, assuming they are otherwise eligible.
• 18 years of age or older
• At present, the potential of AZD2171 for clinically significant drug interactions involving the CYP isozymes is unknown. Eligibility of patients receiving any medication or substances known to affect or with teh potential to affect the activity or PK of AZD2171 will be determined following review of their case by the principal investigator.
• Subjects with treated limited stage basal cell or squamous cell carcinoma of the skin or carcinoma in situ of the breast or cervix are eligible if they otherwise meet eligibility. Subjects with stage I or II cancer treated with curative intent are also eligible with no evidence of recurrent disease.
• No evidence of preexisting uncontrolled hypertension. If patient has hypertension, it must be medically controlled prior to starting AZD2171.
• Women of child-bearing potential must have a negative pregnancy test prior to study entry. Women of child-bearing potential must agree to use adequate contraception prior to study entry and for the duration of study participation.
• No therapeutic anticoagulation. The use of low dose warfarin, intermittent doses of TPA, or heparin flushes to prophylaxis against central venous catheter-associated clots is permitted.
• ECOG Performance status 0-2
• Patients must have normal organ and marrow function as defined in the protocol

Exclusion Criteria:

• Patients who have had chemotherapy, radiotherapy, or major surgery within 3 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 3 weeks earlier.
• Patients may not be receiving any other investigational agents nor have participated in an investigational trial within the past 4 weeks. Prior bevacizumab is allowed.
• Patients may not be receiving any medication that may markedly affect renal function. NSAIDs should be avoided if possible.
• Patients with known brain metastases should be excluded from this clinical trial. A CT of the head is required prior to entry into the study.
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD2171.
• Mean QTc of 470msec or greater in screening electrocardiogram or history of familial long QT syndrome.
• Greater than +1 proteinuria on two consecutive dipsticks taken no less than 1 week apart
• Uncontrolled intercurrent illness including, but not limited to hypertension, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, myocardial infarction cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
• Inability to take and absorb orally administered medication.
• Pregnant women. Breastfeeding should be discontinued.
• Major surgical procedure or medical interference with peritoneum or pleura within 4 weeks of baseline CA-125 assessments. This excludes the need for a paracentesis.
• Subjects with a history of an active malignancy during the last 3 years except non-melanomatous skin cancer, in situ breast or cervical cancer or stage I or II cancer treated with a curative intent and no active cancer recurrence.
• HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with AZD2171.
• New York Heart Association classification of III or IV
• Conditions requiring concurrent use of drugs or biologics with proarrhythmic potential.