In modern vehicle air conditioning concepts, the temperatures at the outlets of the Heating Ventilation and Air Conditioning (HVAC) unit are controlled by an automatic climate control system. Therefore, costly temperature sensors are located in the outlet cross sections of the HVAC unit. A novel coupled Proper Orthogonal Decomposition (POD) and Flow Resistance Network (FRN) approach is proposed to accurately predict the enthalpy flow rates at the outlets of an HVAC unit for real time model based control. For this purpose, the integral enthalpy flow rates at the outlets, which result from a complex mixing process in the mixing chamber of the HVAC unit, are approximated by a linear combination of orthonormal POD modes. Furthermore, a classical FRN is established to compute the volume flow rate at the outlets. By combining the classical FRN with the POD model, the weighting coefficients for the POD modes can be determined from the volume flow rates estimated by the network model. Subsequently, the enthalpy flow rates at the outlets are reconstructed by means of these coefficients. In order to demonstrate the new method on a real HVAC geometry, a test rig is built for the simultaneous measurement of volume flow rates and temperatures at the outlets. The experimental data is further used to perform the POD, to calibrate the FRN and to evaluate the performance of the thermal HVAC model. The major outcome shows that the error of the enthalpy flow rates is less than 10 %, which is considered to be sufficiently accurate. The proposed method delivers a systematic framework to accurately predict the outlet temperatures at low computational costs and eliminates the need for expensive temperature sensors.