We study the potential of a population of thermostatically controlled loads to track desired power signals with provable guarantees. Based on connecting the temperature state of an individual device with its internal energy, we derive necessary conditions that a given power signal needs to satisfy in order for the aggregation of devices to track it using non-disruptive probabilistic switching control. Our derivation takes into account hybrid individual dynamics, an accurate continuous-time Markov chain model for the population dynamics and bounds on switching rates of individual devices. We illustrate the approach with case studies.