Air-solid packed-bed thermal energy storage (PBTES) systems are potential candidates to reduce implementation costs for renewable energy applications. However, heat transfer modelling requires high computational resources, which makes these models unsuitable for control and management in integrated systems. This work presents a fit parameter estimation model to predict the temperature distribution on an operational PBTES system. Through the non-linear least squares method, we use experimental data to calibrate an analytical solution for the heat exchange within an air-solid porous medium. This model presented a normalised root mean squared error of 4% to predict the temperature and the state of charge (SOC). Using mean values from the mass flow rate time series, the model allows estimating the SOC with a deviation of 0.5% from the one calculated from experimental data, and predicted that approximately 60% of the discharged energy was recovered from the storage tank walls, despite not explicitly modelling them. The proposed model avoids solving differential equations by directly computing the analytical solution, making it computationally efficient. Its accuracy and simplicity make it a strong candidate for integration into control and energy management systems for PBTES technologies.