  In the sequel, we extend our previous work on the Minkowski Curve to
Sierpi\'{n}ski simplices (Gasket and Tetrahedron), in the case of the heat
equation. First, we build the finite difference scheme. Then, we give a
theoretical study of the error, compute the scheme error, give stability
conditions, and prove the convergence of the scheme. Contrary to existing work,
we do not call for approximations of the eigenvalues.
