Engineering of cooling mechanisms is a bottleneck in nanoelectronics.Whereas thermal exchanges in diffusive graphene are mostly driven by defect assisted acoustic phonon scattering, the case of high-mobility graphene on hexagonal Boron Nitride (hBN) is radically different with a prominent contribution of remote phonons from the substrate. A bi-layer graphene on hBN transistor with local gate is driven in a regime where almost perfect current saturation is achieved by compensation of the decrease of the carrier density and Zener-Klein tunneling (ZKT) at high bias. Using noise thermometry, we show that this Zener-Klein tunneling triggers a new cooling pathway due to the emission of hyperbolic phonon polaritons (HPP) in hBN by out-of-equilibrium electron-hole pairs beyond the super-Planckian regime. The combination of ZKT-transport and HPP-cooling promotes graphene on BN transistors as a valuable nanotechnology for power devices and RF electronics.Energy relaxation in solids is provided by electron-electron interactions and phonon emission. The former give rise to Wiedemann-Franz (WF) heat conduction to the leads. In diffusive graphene, acoustic phonon emission is dominated by three-body electron-phononimpurity supercollisions (SC) at room temperature 1-4 . The case of high-mobility graphene, in spite of its technological interest, has been less investigated. The suppression of supercollisions and the vanishing of Wiedemann-Franz heat conduction at current saturation give rise to strongly out-of-equilibrium electron distributions where new cooling pathways become prominent. Intrinsic optical phonon (OP) cooling is one of those, it was reported at high density 5 and in suspended graphene 6,7 . Another relaxation mechanism involves interlayer Coulomb coupling in decoupled multilayer epitaxial graphene 8 . In supported graphene the coupling to remote polar phonons overwhelms that to OPs 9-12 . The case of hBN supported or encapsulated graphene is emblematic. Firstly, current saturation can be achieved at low fields E (see Ref. 13 ) opening access to the Zener Klein tunneling (ZKT) regime at high field 14,15 . Secondly, hBN is a uniaxial dielectric that sustains hyperbolic phonon-polaritons (HPPs) [16][17][18][19][20][21][22] in the two Reststrahlen (RS) bands hΩ I = 90-100 meV and hΩ II = 170-200 meV. As a marked difference with SiO 2 surface modes, HPPs can efficiently radiate energy across the dielectric layer 17 , avoiding hot-phonon effects and making an efficient thermal bridge between the graphene channel and the metallic gate in nanodevices.