The evolution of unsteady gravitational-capillary convection in a layer of ethyl alcohol with a free surface after sudden electric heating of one of the vertical walls of a rectangular cavity was investigated numerically. The effect of the incoming flow of hot liquid on the time evolution of the temperature field on the opposite thin metal wall of the cavity was investigated. The calculations were carried out by the finite element method in the conjugate two-dimensional formulation with the Prandtl number Pr = 16, and the range of Grashof numbers determined by the heat flux density, 33·103 ≤ Gr ≤ 28·106. It is shown that the maximum local temperature gradients occur on the wall near the liquid-gas interface.