Recent studies of MEMS thermal micro-actuators have shown that simple devices can provide deflection on the order of 10 μm at low voltages. These thermo-mechanical devices operate by differential thermal expansion caused by ohmic heating in the U-shaped beam of the device. We report on a thermal actuator based on asymmetrical thermal expansion of two beams caused by ohmic heating. Because of the intervention of the different heat transfert mode (such as conduction, convection, and radiation), the motion simulation can be complex. This work demonstrates a good comprehension of the phenomena during a Joule heating process for micro-systems and the development of an analytical model and a finite element analysis. Comparisons between theory and experimental results validate the steady-state conditions. Therefore, this actuator has been successfully integrated in an optical bench and allows the displacement of a micro-lens supported by a movable silicon-frame. This optical bench has been tested to realize a tunable Fabry-Perot filter with a 0.8 μm laser diode and reflective mirror of 99%.