  We present experiments on a superconductor-normal metal electron refrigerator
in a regime where single-electron charging effects are significant. The system
functions as a heat transistor, i.e., the heat flux out from the normal metal
island can be controlled with a gate voltage. A theoretical model developed
within the framework of single-electron tunneling provides a full quantitative
agreement with the experiment. This work serves as the first experimental
observation of Coulombic control of heat transfer and, in particular, of
refrigeration in a mesoscopic system.
