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We consider a thermodynamically consistent diffuse interface model
describing two-phase flows of incompressible fluids in a non-isothermal
setting. The model was recently introduced in~\cite{ERS} where existence
of weak solutions was proved in three space dimensions. Here, we
aim at studying the properties of solutions in the two-dimensional
case. In particular, we can show existence of global in time
solutions satisfying a stronger formulation of the model with
respect to the one considered in~\cite{ERS}. Moreover, we can admit
slightly more general conditions on some material coefficients
of the system
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