Embodiments of the invention describe thermostats that use model predictive controls and related methods. A method of controlling a thermostat using a model predictive control may involve determining a parameterized model. The parameterized model may be used to predicted ambient temperature values for an enclosure. A set of radiant heating system control strategies may be selected for evaluation to determine an optimal control strategy from the set of control strategies. To determine the optimal control strategy, a predictive algorithm may be executed, in which each control strategy is applied to the parameterized model to predict an ambient temperature trajectory and each ambient temperature trajectory is processed in view of a predetermined assessment function. Processing the ambient temperature trajectory in this manner may involve minimizing a cost value associated with the ambient temperature trajectory. The radiant heating system may subsequently be controlled according to the selected optimal control strategy.