Steady thermocapillary droplet migration in a uniform temperature gradient combined with a radiation energy source at large Reynolds and Marangoni numbers is studied. To reach a terminal quasisteady process, the magnitude of the radiation energy source is required to preserve the conservative integral thermal flux across the surface. Under a quasisteady state assumption, an analytical result for the steady thermocapillary migration of a droplet at large Reynolds and Marangoni numbers is derived by using the method of matched asymptotic expansions. It is shown that the thermocapillary droplet migration speed increases as the Marangoni number increases, while a radiation energy source with a sine square dependence is provided.