  In the quantum Hall effect (QHE) regime, heat is carried by electrons in the
edge states of Landau levels. Here, we study cooling of hot electrons
propagating along the edge of graphene at the filling factor $\nu=\pm2$,
mediated by acoustic phonons. We determine the temperature profile extended
from a hot spot, where the Hall current is injected into graphene from a
metallic contact, taking into account specifics of boundary conditions for
lattice displacements in graphene in a van der Waals heterostructure with an
insulating substrate. Our calculations, performed using generic boundary
conditions for Dirac electrons, show that emission of phonons can explain a
short cooling length observed in graphene-based QHE devices by Nahm, Hwang and
Lee [PRL 110, 226801 (2013)].
