We use the inchworm Quantum Monte Carlo method to investigate the full
counting statistics of particle and energy currents in a strongly correlated
quantum dot. Our method is used to extract the heat fluctuations and entropy
production of a quantum thermoelectric device, as well as cumulants of the
particle and energy currents. The energy--particle current cross correlations
reveal information on the preparation of the system and the interplay of
thermal and electric currents. We furthermore demonstrate the signature of a
crossover from Coulomb blockade to Kondo physics in the energy current
fluctuations, and show how the conventional master equation approach to full
counting statistics systematically fails to capture this crossover
