An analysis is made for the transient response behavior of the both, outer and inner, thermal boundary layers of a fluid sphere moving at constant acceleration with internal circulation in an other viscous fluid of large extent initially at rest under the condition of large Reynolds and Peclet numbers. The disturbance is initiated by a step change in temperature of either the continuous or disperse region fluids. The approximate solutions of the governing energy equations are found by using the inviscid approximations for the flow fields.