  In this paper, we demonstrate a set of fundamental conditions required for
the formulation of a thermohydrodynamic lattice Boltzmann model at an arbitrary
Prandtl number. A specific collision operator form is then proposed that is in
compliance with these conditions. It admits two independent relaxation times,
one for viscosity and another for thermal conductivity. But more importantly,
the resulting thermohydrodynamic equations based on such a collision operator
form is theoretically shown to remove the well known non-Galilean invariant
artifact at non-unity Prandtl numbers in previous thermal lattice Boltzmann
models with multiple relaxation times.
