Apparatus and methods are disclosed for coordination of a population of Thermostatically Controlled Loads (TCLs) with unknown parameters to achieve group objectives including bidding and market clearing strategies designed to motivate self-interested users to realize efficient energy allocation subject to a peak power constraint. In one examples of the disclosed technology, a method of operating a load includes estimating a set of values for unmeasured parameters of the load's thermal environment based on output measurements of the thermal environment, determining an energy response based on the estimated set of values for the unmeasured parameters, and transmitting a bid for power for a finite time period based on the determined energy response to the coordinator. A clearing price is received from the coordinator responsive to the transmitted bid and power is sent to the load responsive to the received clearing price.