The behaviour of the thermal boundary layer in an unsteady stagnation flow is studied. The solution of this problem implies the preliminary determination of the velocity distribution of the fluid flow. To solve the problem, a variational approach is proposed. Starting from Lebon-Lambermont's variational criterion and using Kantorovitch's partial integration method, one determines approximate expressions for the temperature boundary thickness. The temperature profiles as well as the heat transfer into the fluid have been expressed in terms of the dimensionless numbers of Peclet, Eckert and Prandtl. Numerical results for two particular media, mercury and viscous oil, are given. © Copyright by Walter de Gruyter & Co.