To improve energy efficiency, the process engineering industry is increasingly tending towards an application of model-based control and diagnosis approaches. Consequently, mathematical models are required that, on the one hand, describe the technical process with sufficient accuracy, but on the other hand do not require too much computational effort. In this regard, the reduction of a model describing the behaviour of a highly viscous, non-isothermal fluid with a free surface is considered. The fluid is modelled by a system of partial differential equations. This system includes both the Navier-Stokes equations and the thermal energy equation describing the temperature behaviour. Using perturbation theory it is shown that the velocities and the temperature of the fluid can be modelled by two reduced models, denoted as submodels. The first submodel is used to calculate the flow dynamics, while the second submodel determines the thermal behaviour.