  Heat transport in the quantum Rabi model at weak interaction with the heat
baths is controlled by the qubit-oscillator coupling. Universality of the
linear conductance versus the temperature is found for $T\lesssim T_K$, with
$T_K$ a coupling-dependent Kondo-like temperature. At low temperature, coherent
heat transfer via virtual processes yields a $\sim T^3$ behavior with
destructive interference in the presence of quasi-degeneracies in the spectrum.
As the temperature increases, incoherent emission and absorption dominate and a
maximum is reached at $T\sim T_K/2$. In the presence of a bias on the qubit,
the conductance makes a transition from a resonant to a broad, zero-bias peak
regime. Parallels and differences are found compared to the spin-boson model in
[K. Saito and T. Kato, Phys. Rev. Lett. \textbf{111}, 214301 (2013)], where the
qubit-bath coupling instead of the internal qubit-oscillator coupling rules
thermal transport.
