A method of generating a thermodynamic model of a structure associated with a heating, ventilation, and air conditioning (HVAC) system, the method comprising: receiving a request for a thermodynamic model of a structure that predicts an indoor temperature trajectory of the structure in response to application of an HVAC actuation state; acquiring time information, temperature information, and HVAC actuation state information for a period of time during which the HVAC system controls a thermal environment of the structure; determining a plurality of weighting factors corresponding to a respective plurality of predetermined basis functions, the weighted combination of basis functions characterizing an indoor temperature trajectory of the structure in response to a change in the HVAC actuation state, characterized by the basis functions including 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, wherein the inertial carryover component dominates at the beginning of a current cycle and eventually disappears, wherein the inertial carryover component is: proportional to an initial rate of temperature change at a beginning of the current cycle; and inversely proportional to an exponential decay with a time constant that represents a difference between an elapsed time since the beginning of the current cycle and an estimated time in the current cycle that steady-state activity begins to overcome early-cycle activity; and in response to the request, returning a thermodynamic model including the determined plurality of weighting factors corresponding to the respective plurality of predetermined basis functions. receiving a request for a thermodynamic model of a structure that predicts an indoor temperature trajectory of the structure in response to application of an HVAC actuation state; acquiring time information, temperature information, and HVAC actuation state information for a period of time during which the HVAC system controls a thermal environment of the structure; determining a plurality of weighting factors corresponding to a respective plurality of predetermined basis functions, the weighted combination of basis functions characterizing an indoor temperature trajectory of the structure in response to a change in the HVAC actuation state, characterized by the basis functions including 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, wherein the inertial carryover component dominates at the beginning of a current cycle and eventually disappears, wherein the inertial carryover component is: proportional to an initial rate of temperature change at a beginning of the current cycle; and inversely proportional to an exponential decay with a time constant that represents a difference between an elapsed time since the beginning of the current cycle and an estimated time in the current cycle that steady-state activity begins to overcome early-cycle activity; and in response to the request, returning a thermodynamic model including the determined plurality of weighting factors corresponding to the respective plurality of predetermined basis functions.