Due to their high energy density and favorable load-to-weight ratio, shape-memory alloy (SMA) materials are ideal actuation sources for soft robots. However, the relatively long cooling time of SMA wires in soft bodies limits their response speed. In this study, we designed and fabricated a novel SMA artificial muscle. When active heat absorption was enabled through thermoelectric modules and the evaporation/dehydration effects of hydrogels, the cooling rate of the SMA wires increased significantly. Simulation and experimental results demonstrate that with the proposed heat-dissipation scheme, the cooling speed of the SMA wires improved notably, with a temperature drop of 9.6 °C within 4 s. Additionally, the designed agar/polyacrylamide hydrogel, which has a porous skeleton structure, achieved a water-absorption expansion rate that was 600% of the previous value. When a PVC elastic substrate was used, the bending angle of the SMA artificial muscle reached 71°, with minimal bending attenuation after 45 consecutive cyclic tests. A soft gripper composed of the novel SMA artificial muscles was capable of manipulating objects of various shapes. Overall, the combination of active and passive heat-dissipation strategies enabled the SMA artificial muscle to achieve excellent durability, rapid heat dissipation, and strong versatility, demonstrating its significant potential for various applications.