The invention relates to a motor vehicle air-conditioning assembly provided with a supercritical fluid refrigerant circuit and comprising a pressure relief member (12) defining a cross-section of fluid flow. The assembly comprises an electronic control device (401) for interacting with the fluid refrigerant circuit. The electronic control device includes a computing function using an estimation of the cross-section of flow of the pressure relief member, the density coefficient of the fluid refrigerant, and the pressure of the fluid refrigerant at the inlet of the pressure relief member for calculating an estimation of the mass flow rate of the fluid refrigerant in the pressure relief member (12).