  We derive a class of thermodynamically consistent variants of
Maxwell/Oldroyd-B type models for viscoelastic fluids. In particular, we study
the models that allow one to consider temperature dependent material
coefficients. This naturally calls for the formulation of a temperature
evolution equation that would accompany the evolution equations for the
mechanical quantities. The evolution equation for the temperature is explicitly
formulated, and it is shown to be consistent with the laws of thermodynamics
and the evolution equations for the mechanical quantities. The temperature
evolution equation contains terms that are ignored or even not thought of in
most of the works dealing with this class of fluids. The impact of the
additional terms in the temperature evolution equation on the flow dynamics is
documented by the solution of simple initial/boundary value problems.
