Our aim in this paper is to study a generalization of the Caginalp phasefield
system based on the theory of type III thermomechanics with two temperatures for the heat conduction. In particular, we obtain well-posedness results and study the dissipativity of the associated solution operators. We consider here both regular and singular nonlinear terms. Furthermore, we endow the equations with two types of boundary
conditions, namely, Dirichlet and Neumann. Finally, we study the spatial behavior of the solutions in a semi-infinite cylinder, when such solutions exist.