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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 transfer mode (such as conduction, convection and radiation), the motion simulation can be complexed. 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.