We consider a thermodynamically consistent diffuse interface model describing
two-phase flows of incompressible fluids in a non-isothermal setting. This
model was recently introduced in a previous paper of ours, where we proved
existence of weak solutions in three space dimensions. Here, we aim at studying
the mathematical properties of the model in the two-dimensional case. In
particular, we can show existence of global in time strong solutions. Moreover,
we can admit slightly more general conditions on some material coefficients of
the system
