In this paper we study the heat transfer from the bottom of a flume to the viscous fluid flowing in it. In particular, we examine the effect of surface waves on the thermal streaks, the temperature field and the heat transfer of the bottom of the flume, under natural and forced convection. It is shown that, under natural convection conditions, there is a considerable effect of the surface waves on the thermal structure in the near-wall region. In a developed turbulent how this effect is rather small.