A Grey-Box Framework for Modeling Free-Floating Indoor Temperature and Cooling Implications in Residential Buildings in Hot-Arid Regions

In the present paper, a data-driven, physics-informed case study of passive thermal behavior in a two-story residential villa located in Al Rayyan, Qatar, is presented to estimate cooling requirements and inform HVAC scheduling strategies. During the monitoring periods, the villa operated under free-floating conditions with no active cooling, allowing the observed indoor temperature evolution to be attributed primarily to envelope-driven heat gains associated with outdoor conditions and solar irradiation. High-resolution measurements of indoor and outdoor air temperature and relative humidity were collected at 5-minute intervals over multiple summer periods. A low-order grey-box model, formulated in a lumped-capacitance (RC) framework, is developed and validated to predict indoor air temperature dynamics using measured indoor thermal state and a diurnal solar forcing proxy that captures thermal lag effects characteristic of heavy-mass construction. The model demonstrates high short-horizon predictive accuracy and remains stable when applied recursively to simulate indoor temperature evolution without active cooling. Using the validated model, time-resolved comfort metrics and setpoint-dependent cooling implications are quantified, including hours and degree-hours above typical comfort thresholds. The proposed framework provides a practical pathway for translating limited field measurements into simplified predictive models that support cooling capacity assessment and operational decision-making for residential buildings in hot–arid climates.