  In Lipschitz domains, we study a Darcy-Forchheimer problem coupled with a
singular heat equation by a nonlinear forcing term depending on the
temperature. By singular we mean that the heat source corresponds to a Dirac
measure. We establish the existence of solutions for a model that allows a
diffusion coefficient in the heat equation depending on the temperature. For
such a model, we also propose a finite element discretization scheme and
provide an a priori convergence analysis. In the case that the aforementioned
diffusion coefficient is constant, we devise an a posteriori error estimator
and investigate reliability and efficiency properties. We conclude by devising
an adaptive loop based on the proposed error estimator and presenting numerical
experiments.
