In this paper, we consider a slab represented by the interval 0 < x < 1, at the initial temperature u0(x) > 0 and having a heat flux q(t) on the left face and a nonlinear condition on the right face x = 1. We consider the corresponding heat conduction problem and we assume that the phase-change temperature is 0ºC. We prove that certain conditions on the data are necessary and sufficient in order to obtain estimations of the occurrence of a phase-change in the material.