Thermal bimorphs are a popular actuation technology in MEMS (micro-electro-mechanical systems). Their operating principle is based on differential thermal expansion induced by Joule heating. Thermal bimorphs, and other thermal flexure actuators have been used in many applications, from micro-grippers, to micro-optical mirrors. In most cases open-loop control is used to difficulties in fabricating positioning sensors together with actuator. In this paper we present several methods for extracting reduced-order thermal flexure actuator models based on experimental data, physical principles, and FEA simulation. We then use the models to generate optimal driving signals using input shaping techniques. Both simulation and experimental results are included to illustrate the efficacy of our approach. This framework can also be applied to other types of MEMS actuators, including electrostatic comb drives.