Viscoelastic fluids often exhibit high sensitivity of material properties on temperature changes. Nevertheless, the available mathematical theory for these fluids concerns only models that are isothermal or that are simplified in other ways. For example, one can find existence theories in 2D, for small data, with only the corotational derivative, with only the spherical part of the elasticity tensor etc. In the talk, we introduce an existence theory without any of these assumptions and treat a rather general class of Johnson-Segalman-like models including full thermal evolution. To avoid the well-known ill-posedness of the corresponding PDE system, we modify the ``elastic part'' of the dissipation of the fluid far from the equilibrium, while preserving thermodynamic compatibility of the model. This way, we are able to prove the existence of a global-in-time weak solution for any initial datum with finite total energy and entropy.