  Thermal transport in a quasi-ballistic regime is determined not only by the
local temperature $T(r)$, or its gradient $\nabla T(r)$, but also by
temperature distribution at neighboring points. For an accurate description of
non-local effects on thermal transport, we employ the thermal distributor,
$\Theta (r,r')$, which provides the temperature response of the system at point
$r$ to the heat input at point $r'$. We determine the thermal distributors from
the linearized Peierls-Boltzmann equation (LPBE) and the relaxation time
approximation (RTA) of the Peierls-Boltzmann equation and employ them to
describe thermal transport in quasi-ballistic graphene devices.
