We study the demand-response potential from large numbers of appliances which have to maintain some temper- ature within a fixed range through the ON/OFF functioning of a temperature modifier. Based on a mathematical model, we propose methods to coordinate appliances to offer a global energy demand reduction over an imposed duration while still satisfying the appliances’ temperature constraints, and with limited communication overhead. The maximum power reduction that can be attained is ex- pressed mathematically, as a function of the appliances’ speci- ficities and the reduction duration asked by the grid.