  We self-consistently derive a formalism that couples a Phase Field Crystal
(PFC) density field to thermal transport. It yields a theory for non-uniform
transient temperature and density evolution, and includes local latent heat
release during atomic rearrangements of the PFC density field. The basic
formalism is applied to the basic PFC model, demonstrating the approach's
capacity to capture solidification and recalescence. With an aim towards
linking physical temperature to PFC temperature, a new classical density field
theory for solid/liquid/vapor systems is then derived. It presents a different
approach to those traditionally used in the PFC literature while still
retaining the major advantages that have become the hallmark of PFC modelling.
The new model is based entirely on physical density and temperature scales. We
end the paper by applying the thermal-density coupling formalism to this new
multi-phase density functional theory/PFC model.
