  Lattice kinetic equations incorporating the effects of external/internal
force fields via a shift of the local fields in the local equilibria, are
placed within the framework of continuum kinetic theory. The mathematical
treatment reveals that, in order to be consistent with the correct
thermo-hydrodynamical description, temperature must also be shifted, besides
momentum. New perspectives for the formulation of thermo-hydrodynamic lattice
kinetic models of non-ideal fluids are then envisaged. It is also shown that on
the lattice, the definition of the macroscopic temperature requires the
inclusion of new terms directly related to discrete effects. The theoretical
treatment is tested against a controlled case with a non ideal equation of
state.
