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 $N$ interisland 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 $M^2/{(2N+M)}^2$. 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.

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• Coulomb blockade
• Edge states
• Heat transfer
• Integer quantum Hall effect
• Quantum transport
• Double quantum dots
• Two-dimensional electron system
• Langevin equation