A major challenge for upper limb amputees is discomfort due to improper socket fit on the residual limb during daily use of their prosthesis. Our work introduces the implementation of soft robotic actuators into a prosthetic socket. The soft actuators are a type of electrically-powered actuator. The actuator is driven through changes in internal temperature causing actuation due to vapor pressure, which results in high and reliable force outputs. A regression fit was generated to model how the smart polymer's temperature relates to force output, and the model was cross-validated based on training data collected from each actuator. A proportional integral (PI) controller regulated the force exerted by the actuators based off of tactile and temperature feedback. Results showed that a socket system can be integrated with smart polymers and sensors, and demonstrated the ability to control two actuators and reach desired forces from set temperatures.