  We evaluate the thermal torques exerted on low-mass planets embedded in
gaseous protoplanetary discs with thermal diffusion, by means of
high-resolution three-dimensional hydrodynamics simulations. We confirm that
thermal torques essentially depend on the offset between the planet and its
corotation, and find a good agreement with analytic estimates when this offset
is small compared to the size of the thermal disturbance. For larger offsets
that may be attained in discs with a large pressure gradient or a small thermal
diffusivity, thermal torques tend toward an asymptotic value broadly compatible
with results from a dynamical friction calculation in an unsheared medium. We
perform a convergence study and find that the thermal disturbance must be
resolved over typically 10 zones for a decent agreement with analytic
predictions. We find that the luminosity at which the net thermal torque
changes sign matches that predicted by linear theory within a few percents. Our
study confirms that thermal torques usually supersede Lindblad and corotation
torques by almost an order of magnitude for low mass planets. As we increase
the planetary mass, we find that the ratio of thermal torques to Lindblad and
corotation torques is progressively reduced, and that the thermal disturbance
is increasingly distorted by the horseshoe flow. Overall, we find that thermal
torques are dominant for masses up to an order of magnitude larger than
implemented in recent models of planetary population synthesis. We finally
briefly discuss the case of stellar or intermediate-mass objects embedded in
discs around AGNs.
