  The evolution of the power grid towards the so-called Smart Grid, where
information technologies help improve the efficiency of electricity production,
distribution and consumption, allows to use the fine-grained control brought by
the Internet of Things capabilities to perform distributed demand response when
requested by the grid. In this paper, we study the demand-response potential of
coordinated large numbers of appliances which have to maintain some temperature
within a fixed range through the ON/OFF functioning of a temperature modifier.
We introduce a mathematical model and methods to coordinate appliances with
given requirements, in order to offer a global energy demand reduction for a
desirable duration while still satisfying the temperature constraints, and with
limited communication overhead. We quantify the maximum power reduction that
can be attained, as a function of the reduction duration asked by the grid.
