We argue that surface undulations observed after self-sustained rapid crystallization of amorphous films result from a thermal instability that induces a periodically varying crystallization rate. Its physical origin is discussed for a simple nonlinear heat conduction model which yields good agreement with experimental observations. The model displays a rich variety of interesting physical phenomena. It contains a co-dimension two bifurcation point in whose vicinity detailed analytic results can be obtained. A numerical analysis of the nonlinear oscillations shows that these, in turn, bifurcate via a series of period-doubling bifurcations.