An environmental control system for a building including heating, ventilation, or air conditioning (HVAC) equipment that operates to affect a zone of the building and a controller including a processing circuit. The processing circuit is configured to estimate a thermal resistance between air of the zone and of an external space using values of a temperature of the zone air, a temperature of the external space air, and a heat transfer rate of the HVAC equipment, each value corresponding to a different time step within a time period. The processing circuit is configured to use the thermal resistance, time step specific values of the temperatures, and time step specific values of the heat transfer rate to estimate corresponding values of a heat disturbance. The processing circuit is configured to operate the HVAC equipment using a model-based control technique based on the heat disturbance values.