In modern vehicle air conditioning concepts, the temperatures at the outlets of the Heating Ventilation and Air Conditioning (HVAC) unit are controlled using temperature sensors in combination with an Automatic Climate Control (ACC) system. A novel coupled Proper Orthogonal Decomposition (POD) and Flow Resistance Network (FRN) model approach is proposed to accurately predict the temperatures at the outlets of a HVAC unit for real-time model based control. 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. A FRN is established to compute the volume flow rates 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. This allows to reconstruct the enthalpy flow rates at the outlets and to calculate the outlet temperatures. 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 used to perform the POD, to calibrate the FRN and to evaluate the performance of the thermal HVAC model. The proposed method provides a systematic framework to accurately predict the outlet temperatures at low computational costs. It could be shown that the absolute temperature deviation between model and experiment at the outlets is less than 2 K. An inverse application of the model for climate control was demonstrated. Instead of using expensive temperature sensors, the model can be applied for model based ACC which reduces costs and facilitates control algorithms.