  We consider a quantum dot system whose charge fluctuations are monitored by a
quantum point contact allowing for the detection of both charge and transferred
heat statistics. Our system consists of two nearby conductors that exchange
energy via Coulomb interaction. In interfaces consisting of capacitively
coupled quantum dots, energy transfer is discrete and can be measured by charge
counting statistics. We investigate gate dependent deviations away from a
charge fluctuation theorem in the presence of local temperature gradients (hot
spots). Non universal relations are found for state dependent charge counting.
A fluctuation theorem holds for coupled dot configurations with heat exchange
and no net particle flow.
