We study, both theoretically and experimentally, the features on the current-voltage characteristic of a highly transparent Josephson junction caused by transition of the superconducting leads to the normal state. These features appear due to the suppression of the Andreev excess current. We show that by tracing the dependence of the voltage, at which the transition occurs, on the bath temperature and by analyzing the suppression of the excess current by the bias voltage one can recover the temperature dependence of the heat flow out of the junction. We verify theory predictions by fabricating two highly transparent superconductor-graphene-superconductor (SGS) Josephson junctions with suspended and nonsuspended graphene as a nonsuperconducting section between Al leads. Applying the above mentioned technique we show that the cooling power of the suspended junction depends on the bath temperature as â Tbath3.1 close to the superconducting critical temperature.