  We present a new type of calorimeter in which we couple an unknown heat
capacity with the aid of Peltier elements to an electrical circuit. The use of
an electrical inductance and an amplifier in the circuit allows us to achieve
autonomous oscillations, and the measurement of the corresponding resonance
frequency makes it possible to accurately measure the heat capacity with an
intrinsic statistical error that decreases as ~t^{-3/2} with measuring time t,
as opposed to a corresponding error ~t^{-1/2} in the conventional alternating
current (a.c.) method to measure heat capacities. We have built a demonstration
experiment to show the feasibility of the new technique, and we have tested it
on a gadolinium sample at its transition to the ferromagnetic state.
