This article presents an exploratory process of finding root causes of an undesirable pressure imbalance in an industrial high temperature heat pump based on a reverse Stirling engine using a simulation model of the process. Different types of Stirling engine configurations can be used as heat engines converting heat to power or as heat pumps using power to raise the temperature of low temperature heat to a higher level. The studied heat pump has a double-acting α-configuration, with two double-acting pistons interacting with a working fluid on each piston face. Theoretically, this configuration creates two separate circuits, which can be treated in isolation of each other, but in practice, some working fluid will leak through the piston rings. A simulation model of the studied Stirling system using the software Simulink was developed to investigate to which degree such piston-ring leakages could affect system pressures. By modelling piston-ring leakage and experimenting with different combinations of model parameters, different types of effects on system pressures are seen in the simulations, offering explanations for pressure fluctuations observed in the real heat pump system. These pressure phenomena may well be present in other reciprocating systems, and identifying them is a first step in preventing them in order to increase system stability. An interesting observation was that the direction of the imbalance was not necessarily determined by the direction of the leak through the piston rings, but by the piston position at the onset of the leak. The simulation model is shown to be capable of reproducing complex patterns seen in the measurements of the real process by simple modifications and adaptation of model parameters.