An analysis is presented of the flow in a layer of liquid whose surface tension varies under the action of a moving surface heat flux distribution chosen to model the spread of a flame over the liquid. Subject to this heat flux, the surface temperature increases from the ambient temperature of the liquid, far upstream, to its vaporization temperature at a moving vaporization front, and stays constant at this value downstream of the vaporization front. The speed of the front is determined by a condition of regularity of the temperature. Three different regimes are found which correspond to the uniform, pulsating and pseudo-uniform regimes of flame spread observed experimentally when the ambient temperature of the liquid, or the strength of the surface heat flux, is decreased. The first and third of these are stationary regimes of high and low front speed, and the second is an oscillatory regime featuring long phases of low speed and short pulses of high speed. An asymptotic description is given of the flow relative to the moving vaporization front in the stationary regime of low speed, which includes a long recirculation eddy ahead of the front and a small region around the front that controls its speed. An explanation of the mechanism of oscillation is proposed based on the interplay between the quasi-steady response of this small controlling region and the delay introduced by the recirculating flow.