Temperature-dependent characteristics of GeSn/Ge multiple-quantum-well (MQW) photoconductors (PCs) on silicon substrate were investigated. The high quality GeSn/Ge MQW epitaxial structure was grown on a silicon substrate using low temperature molecular beam epitaxy techniques with atomically precise thickness control. Surface-illuminated GeSn/Ge MQW PCs were fabricated using complementary metal-oxide-semiconductor-compatible processing and characterized in a wide temperature range of 55-320 K. The photodetection range was extended to λ=2235nm at T=320K due to bandgap shrinkage with Sn alloying. Measured spectral responsivity was enhanced at reduced temperatures. These results provide better understanding of GeSn/Ge MQW structures for efficient short-wave infrared photodetection.