  The Wiedemann-Franz law, connecting the electronic thermal conductivity to
the electrical conductivity of a disordered metal, is generally found to be
well satisfied even when electron-electron (e-e) interactions are strong. In
ultra-clean conductors, however, large deviations from the standard form of the
law are expected, due to the fact that e-e interactions affect the two
conductivities in radically different ways. Thus, the standard Wiedemann-Franz
ratio between the thermal and the electric conductivity is reduced by a factor
$1+\tau/\tau_{\rm th}^{\rm ee}$, where $1/\tau$ is the momentum relaxation
rate, and $1/\tau_{\rm th}^{\rm ee}$ is the relaxation time of the thermal
current due to e-e collisions. Here we study the density and temperature
dependence of $1/\tau_{\rm th}^{\rm ee}$ in the important case of doped, clean
single layers of graphene, which exhibit record-high thermal conductivities. We
show that at low temperature $1/\tau_{\rm th}^{\rm ee}$ is $8/5$ of the
quasiparticle decay rate. We also show that the many-body renormalization of
the thermal Drude weight coincides with that of the Fermi velocity.
