In this paper the problem of a thermal laminar magnetohydrodynamic (MHD) boundary layer with suction developing from rest around a body is studied. The analysis includes the case of small temperature differences, when the wall temperature is constant, as well as for the small values of the magnetic Reynolds number. Supposing a priori that the velocity of the external flow can be developed in series of y/t, it is then shown that the various quantities characterizing both dynamic and thermal unsteady boundary layers can be determined by a power series expansion of \ft. Finaly, as a particular case, the thermal MHD boundary layer with suction on a uniformly accelerated cylindrical body and for the Prandtl number equal to unity is calculated.