We introduce a non-isothermal phase-field crystal model including heat flux and thermal expansion of the crystal lattice. The fundamental thermodynamic relation between internal energy and entropy, as well as entropy production, is derived analytically and further verified by numerical benchmark simulations. Furthermore, we examine how the different model parameters control density and temperature evolution during dendritic solidification through extensive parameter studies. Finally, we extend our framework to the modeling of open systems considering external mass and heat fluxes. This work sets the ground for a comprehensive mesoscale model of non-isothermal solidification including thermal expansion within an entropy-producing framework, and provides a benchmark for further meso- to macroscopic modeling of solidification.