An Invar-based dual Fabry-Pérot cavity refractometer used for assessments of pressure by the gas modulation refractometry (GAMOR) methodology has been scrutinized with respect to the influence of thermodynamic effects (pV-work) that originates from the gas exchange process when 100 kPa of nitrogen is addressed. It is shown that the actual temperature variation of the cavity spacer solely is a fraction of the previously assessed upper limits (0.5 mK/100 kPa), limited to sub-parts-permillion (ppm) levels. This finding additionally supports the conclusion that the thermodynamic effects will not be a limiting factor when the system is used for assessments of pressure.