  We theoretically study the Coulomb drag in graphene when there is a
temperature difference between the layers. Within the degenerate limit for
equal layer densities, we find that this can lead to significant deviations
from the usual quadratic temperature dependence of the drag resistivity. The
exact behavior depends strongly on the phase space available for intraband
scattering, and is not symmetrical when the temperatures of the layers are
interchanged. In particular, when one layer is at a much higher temperature $T$
than the other, the drag resistivity behaves as $\rho_D\sim T/d^5$, where $d$
is the interlayer separation. The magnitude of the drag in this limit is always
larger when the active layer is at the higher temperature.
