The onset of Marangoni convection in an initially quiescent spherical droplet subjected to the impulsive change in boundary temperature is analyzed under the linear theory. For this system in which instabilities are driven by interface-tension gradients, a stability analysis on regular cell modes is conducted on the basis of the propagation theory we have developed. The present stability analysis predicts that τc decreases with increasing Ma. For the limiting case of τ →0, the present study approaches the planar limit as expected.