Abstract
We study the thermal transport properties of a mesoscopic device comprising two metallic islands embedded in a two-dimensional electron gas in the integer quantum Hall regime. It is shown that the 2M ballistic edge channels connecting the islands to the external reservoirs and the N inter-island channels play a central role in the phenomenon of heat Coulomb blockade. Unlike the single-island case, where the heat flux is reduced by exactly one quantum of thermal conductance, we predict an additional suppression proportional to the factor M²/(2N+M)². We further examine a configuration in which the islands are placed between electrodes at different temperatures and identify the conditions under which the Wiedemann-Franz law is violated.