Thermostats disclosed herein are operable to control an HVAC system. In controlling the HVAC system, a need to determine an expected indoor temperature profile for a particular schedule of setpoint temperatures may arise. To make such a determination, a thermodynamic model of the structure is used. The thermodynamic model may be generated by fitting weighting factors of a set of basis functions to a variety of historical data including time information, temperature information, and HVAC actuation state information. The set of basis functions characterize an indoor temperature trajectory of the structure in response to a change in HVAC actuation state, and include an inertial carryover component that characterizes a carryover of a rate of indoor temperature change that was occurring immediately prior to the change in actuation state.