A quasi-analytical solution of the conjugated heat transfer problem for a semi-infinite flat plate that is impulsively accelerated in a compressible laminar flow with Prandtl number equal to 1 is proposed. The solution is based on an integral formulation both for the momentum and energy equations in the fluid and for the thermal coupling between the fluid and the solid. The results are compared to previously obtained exact solutions in the limiting conditions of ＇asymptotic＇ and ＇steady＇ flow. The influence on the temperature field of the main parameters characterizing the problem is discussed, (C) 2000 Elsevier Science Ltd. All rights reserved.