  We study the energy and temperature relaxation of electrons in graphene on a
piezoelectric substrate. Scattering from the combined potential of extrinsic
piezoelectric surface acoustical (PA) phonons of the substrate and intrinsic
deformation acoustical (DA) phonons of graphene is considered in a
(non-)degenerate gas of Dirac fermions. It is shown that in the regime of low
energies or temperatures the PA phonons dominate the relaxation and change
qualitatively its character. This prediction is relevant for quantum metrology
and electronic applications using graphene devices and suggests a new
experimental setup for probing electron-phonon coupling in graphene.
