This is a Phase 1b, open-label, dose-finding study of tivozanib (AV-951) in combination with temsirolimus to include approximately 36 subjects with metastatic renal cell carcinoma (mRCC). This study is designed to evaluate the safety, tolerability, dose-limiting toxicities (DLT), maximum tolerated dose (MTD), pharmacokinetic, pharmacogenomic, and antineoplastic activity of tivozanib (AV-951) when administered in combination with temsirolimus. Tivozanib (AV-951) will be administered once daily for 3 weeks beginning on Day 1 of Cycle 1, followed by 1 week off (1 cycle = 4 weeks). Temsirolimus will be administered intravenously once weekly starting on Day 8 of Cycle 1.