This paper utilizes a computational approach to address the effect of bubble deformation on the transient thermocapillary migration of bubbles in a microgravitational environment. We use a finite volume method with interface tracking capability on a moving unstructured mesh. We consider a range of Reynolds and Marangoni numbers from 1 to 100 and a range of capillary numbers from 0.001 to 0.1. The transient migration of bubbles in which bubble deformation is significant is described.