Many aspects of high temperature electrolysis cell operation have been studied experimentally in recent years, including the freezing and melting of electrolyte, the dissolution of added solute material, replacement of anodes and the degradation of the cell’s top crust. The present paper reviews this work for the specific case of aluminium electrolysis cells and describes a mathematical model for the cell enthalpy balance which allows the combined effect of all the process kinetics to be observed over time. Comparison of model predictions with dynamic industrial cell measurements is performed where possible, and this demonstrates the importance of interfacial heat transfer from the electrolyte to the cell walls and to feed materials - alumina and anode carbon. The model is then applied to the analysis of generic energy imbalances in a modern industrial electrolysis cell. The causes of these energy imbalances are identified and the consequences for cell performance are predicted using the model. Key issues in the modelling of electrolysis cells identified from these applications, include the importance of different time-scales in mathematically stiff systems, and the unusual behaviour of electrolyte superheat under certain energy imbalance conditions.