We investigate energy relaxation in a high-mobility graphene on BN transistors. Above a threshold bias voltage, the transistor is driven in a Zener-Klein tunnelling regime involving the creation of electron-hole pairs. Simultaneously, we record the electron gas temperature by means of high sensitivity GHz noise thermometry. We show that a new -extremely efficient- cooling mechanism sets in at the Zener-Klein bias threshold that we assign to the relaxation of electron-hole pairs to hyperbolic polariton modes sustained by the BN substrate. The most striking consequence is a reversal of the doping dependence of the electronic temperature due to the Pauli blocking of ZK-tunnelling at finite doping. HPP cooling is the most efficient mechanism in graphene and promotes graphene Zener-Klein transistors as a valuable route for RF power amplification.