Shape Memory Alloys (SMA) are characterized by a unique solid-solid phase transition during which significant strains are observable. On reversal of this phase transition, the strains also are almost completely recoverable. When properly constrained, a shape memory alloy is capable of producing large actuation forces. The frequency of actuation, however, depends on the heat transfer mechanism employed. Here, we undertake a theoretical study of a heat removal approach using semiconductors. These solid state elements employ the thermoelectric Peltier Effect for cooling or heating of the SMA. Compared to free or forced convection cooling mechanisms, cooling by the Peltier Effect is significantly faster. The phase transition is accompanied by a significant exchange of latent heat, and it is seen that the time period for a complete thermal cycle with the phase transition almost doubles as opposed to one without a phase transition. Partial phase transformation results in a lower period of cycling: 25% of transformation translates to the time period being 30% of the one with full transformation. AS a first step in the design of the actuator, a thermoelectric module is assembled in the laboratory for cooling/heating the SMA. Transient temperature profiles are recorded for the heating and cooling runs for two different materials--copper and SMA (with or without the phase transformation). These recorded profiles are then compared with the predictions from the model; the agreement is reasonable, particularly during the cooling process.