A system includes a plurality of thermostats corresponding to a plurality of HVAC systems that serve a plurality of spaces and a computing system communicable with the plurality of thermostats via a network. The computing system is configured to, for each space of the plurality of spaces, obtain a set of training data relating to thermal behavior of the space, identify a model of thermal behavior of the space based on the set of training data, perform a model predictive control process using the model of thermal behavior of the space to obtain a temperature setpoint for the space, and provide the temperature setpoint to the thermostat corresponding to the HVAC system serving the space. The plurality of thermostats are configured to control the plurality of HVAC systems in accordance with the temperature setpoints.