The thermodynamics of the air inside a conventional Oscillating Water Column (OWC) is commonly modelled using the isentropic relationship between pressure and density. The innovative Tupperwave device is based on the OWC concept but uses non-return valves and two extra reservoirs to rectify the flow into a smooth unidirectional air flow harnessed by a unidirectional turbine. The air, flowing in closed-circuit, experiences a temperature increase due to viscous losses across the valves and turbine along the repetitive cycles of the device's operation. In order to study this temperature increase which represents a potential issue for the device operation, a non-isentropic wave-to-wire model of the Tupperwave device is developed taking into account the irreversible thermodynamic processes. The model is based on the First Law of Thermodynamics, and accounts for viscous losses at the valves and turbine as well as solar radiation and heat transfer across the device walls and inner free-surface. The results reveal that the temperature increase in the device remains harmless for its operation. The difference between the power performance of the Tupperwave device based on the non-isentropic and isentropic models is found to be relatively small. Its performance are also compared to the corresponding conventional OWC device.