We study the effect of the p-Laplacian operator in the modelling of the heat equation through a porous medium. The case of p = 2 was recently published in (Anguiano, Mediterr. J. Math. 17, 18 (2020)). Using rigorous functional analysis techniques and the properties of Sobolev spaces, we managed to solve additional (nontrivial) difficulties which arise compared to the study for p = 2, and we prove a convergence theorem in appropriate functional spaces.