The problem of the motion induced by a sinusoidal thermal wave propagating in a horizontal layer of fluid is investigated in the limit of small Prandtl number. An exact solution of the nonlinear equations is derived in a special case. The mean flow corresponding to this particular solution is vanishing for all values of the wavenumber, the phase speed, and the amplitude of the wave. More general solutions with non-vanishing mean flow are obtained by a perturbation approach based on the exact solution. In addition it is found that mean flows of either sign occur in the form of an instability, even in the case when the temperature field is stationary.