On thermodynamics of viscoelastic rate type fluids with temperature   dependent material coefficients
  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. 
Jaroslav Hron and Vojt\v{e}ch Milo\v{s} and V\'it Pr\r{u}\v{s}a and   Ond\v{r}ej Sou\v{c}ek and Karel T\r{u}ma
physics.flu-dyn