Actuators are widely used in various mechanical products. However, there have been no actuators that can exhibit high actuation stresses and strains at cryogenic temperatures. Although shape memory alloys (SMAs) are attractive candidates for thermally driven actuators with high actuation stresses and strains, the operation of conventional SMAs is limited to a narrow temperature range near the room temperature. Here, we report the shape memory effect under tensile conditions with a high work output across a wide temperature range of 50–270 K in Cu-Al-Mn-based alloys. In addition, a mechanical heat switch using Cu-Al-Mn was designed for thermal insulation in space infrared telescope, and we demonstrated the operation at around 100 K. These results indicate that Cu-Al-Mn SMAs are potential cryogenic actuators with high actuation stress and strain that would contribute to the development of low temperature technologies in various fields including space astronomy, superconductivity, and liquefied gas industry.