A thermostat comprising: a memory; and a processing system that is in operative communication with the memory and with a radiant heating system, the processing system being configured and programmed to control the radiant heating system according to the steps of: determining a parameterized model from which a temperature response of an enclosure responsive to a candidate radiant heating control strategy may be determined, the parameterized model being based at least in part on historical temperature information stored in said memory and acquired during at least one historical period in which the enclosure was heated by the radiant heating system under the control of said thermostat, the thermostat being characterized in that the processing system is further configured and programmed to control the radiant heating system according to the steps of: determining an optimal radiant heating control strategy from among a plurality of candidate radiant heating control strategies by applying each candidate radiant heating control strategy to the parameterized model to predict a corresponding ambient temperature trajectory and processing each corresponding ambient temperature trajectory according to one or more predetermined assessment criteria to select an optimal one of the plurality of candidate radiant heating control strategies as the optimal radiant heating control strategy according to the one or more predetermined assessment criteria; and controlling the radiant heating system according to the determined optimal radiant heating control strategy. a memory; and a processing system that is in operative communication with the memory and with a radiant heating system, the processing system being configured and programmed to control the radiant heating system according to the steps of: determining a parameterized model from which a temperature response of an enclosure responsive to a candidate radiant heating control strategy may be determined, the parameterized model being based at least in part on historical temperature information stored in said memory and acquired during at least one historical period in which the enclosure was heated by the radiant heating system under the control of said thermostat, the thermostat being characterized in that the processing system is further configured and programmed to control the radiant heating system according to the steps of: determining an optimal radiant heating control strategy from among a plurality of candidate radiant heating control strategies by applying each candidate radiant heating control strategy to the parameterized model to predict a corresponding ambient temperature trajectory and processing each corresponding ambient temperature trajectory according to one or more predetermined assessment criteria to select an optimal one of the plurality of candidate radiant heating control strategies as the optimal radiant heating control strategy according to the one or more predetermined assessment criteria; and controlling the radiant heating system according to the determined optimal radiant heating control strategy. determining an optimal radiant heating control strategy from among a plurality of candidate radiant heating control strategies by applying each candidate radiant heating control strategy to the parameterized model to predict a corresponding ambient temperature trajectory and processing each corresponding ambient temperature trajectory according to one or more predetermined assessment criteria to select an optimal one of the plurality of candidate radiant heating control strategies as the optimal radiant heating control strategy according to the one or more predetermined assessment criteria; and controlling the radiant heating system according to the determined optimal radiant heating control strategy.