A nonlinear system identification approach was used to exploit the nonlinearly in the exergy of the system and reduce it into two or more interconnected elements. The Hammerstein–Wiener (H-W) methodology was adopted to describe the dynamics of a passive thermal system using a combination of nonlinear and linear blocks. Here, the linear block is a discrete transfer function, which symbolizes the dynamic component of the model. The proposed model was validated using the state functions measured for the solar air collector. The mean absolute percentage error (MAPE) for enthalpy changes falls in the domain of −0.01% to 0.01%, whereas it varied from −0.06% to 0.02% as the entropy of the system changed with time. Similarly, the MAPE encountered while evaluating the exergy of the system was in the closed interval of −0.066% to −0.0017%. The average exergy gain by the H-W model across the Ist and IInd passages was, respectively, 0.90 kJ · kg−1 (8.10 g · s−1), 0.61 kJ · kg−1 (10.10 g · s−1) and 0.46 kJ · kg−1 (12.10 g · s−1); and 0.57 kJ · kg−1 (8.10 g · s−1), 0.48 kJ · kg−1 (10.10 g · s−1), and 0.79 kJ · kg−1 (12.10 g · s−1). The proposed model exhibited good fitting with the validation data.