A level-set method is presented for computing microdroplet evaporation on a heated surface. The formulation based on a sharp-interface representation for incompressible two-phase flow is extended to include the effect of evaporation by employing a calculation procedure for the coupled interface conditions for the temperature and mass fraction. A dynamic contact angle model is also incorporated into the level-set method to account for the change between advancing and receding contact angles at the liquid-gas-solid interline. The numerical method is applied to analyze the effect of wall temperature, contact angle and droplet size on the microdroplet motion.