Direct internal reforming enables optimal heat integration and reduced complexity in solid oxide fuel cell (SOFC) systems, but thermal stresses induced by the increased temperature gradients may inflict damage to the stack. Therefore, the development of adequate control strategies requires models that can accurately predict the temperature profiles in the stack. A 1D dynamic modelling platform is developed in this study, and used to simulate SOFCs in both single cell and stack configurations. The single cell model is used to validate power law and Hougen-Watson reforming kinetics derived from experiments in previous work. The stack model, based on the same type of cells, accounts for heat transfer in the inactive area and to the environment, and is validated with data reported by the manufacturer. The reforming kinetics are then implemented in the stack model to simulate operation with direct internal reforming. Although there are differences between the temperature profiles predicted by the two kinetic models, both are more realistic than assuming chemical equilibrium. The results highlight the need to identify rate limiting steps for the reforming and hydrogen oxidation reactions on anodes of functional SOFC assemblies. The modelling approach can be used to study off-design conditions, transient operation and system integration, as well as to develop adequate energy management and control strategies.