We derive a class of thermodynamically consistent variants of Maxwell/Oldroyd-B type
models for incompressible 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 …