Upon the introdution of gas bubble into a liquid possessing a uniform thermal gradient, an unsteady thermocapillary flow begins. Ultimately, the bubble atains a constant velocity. This theoretial analysis focuses upon the transient period for a bubble in a microgravity environment and is restricted to situations wherein the flow is sufficiently slow such that inertial terms in the Navier‐Stokes equation and convective terms in the energy equation may be safely neglected (i.e., both Reynolds and Marangoni numbers are small). The resulting linear equation were solved analytically in the Laplace domain with the Prandtl number of the liquid as a parameter; inversion was accomplished numerically using a standard IMSL routine. In the asymptotic long‐time limit, our theory agrees with the steady‐state theory of Young, Goldstein, and Block. The theory predicts that more than 90% of the terminal steady velocity is achieved when the smallest dimensionless time, i.e., the one based upon the largest time scale‐viscous or thermal‐equals unity.