The modelling of non-isothermal flow of viscoelastic materials using differential constitutive equations is investigated. The approach is based on the concept of a slip tensor describing the nonaffine motion of the stress-carrying structure of the fluid. By specifying a slip tensor and the elastic behaviour of the structure, the constitutive model is determined. This slip tensor also appears in the energy equation and thus, for a given constitutive model, the form of the energy equation is known. Besides the partitioning between dissipated and elastically stored energy, also the difference between entropy and energy elasticity is discussed. Numerical simulations are based on a stabilized Discontinuous Galerkin method to solve the mass, momentum and constitutive equations and a Streamline Upwind Petrov-Galerkin formulation to solve the energy equation. Coupling is achieved by a fixed point iteration. The flow around a confined cylinder is investigated, showing differences between viscous and viscoelastic modelling, and between limiting cases of viscoelastic modelling.