  By means of three dimensional, high resolution hydrodynamical simulations we
study the orbital evolution of weakly eccentric or inclined low-mass
protoplanets embedded in gaseous discs subject to thermal diffusion. We
consider both non-luminous planets, and planets that also experience the
radiative feedback from their own luminosity. We compare our results to
previous analytical work, and find that thermal forces (the contribution to the
disc's force arising from thermal effects) match those predicted by linear
theory within $\sim 20$%. When the planet's luminosity exceeds a threshold
found to be within $10$% of that predicted by linear theory, its eccentricity
and inclination grow exponentially, whereas these quantities undergo a strong
damping below this threshold. In this regime of low luminosity indeed, thermal
diffusion cools the surroundings of the planet and allows gas to accumulate in
its vicinity. It is the dynamics of this gas excess that contributes to damp
eccentricity and inclination. The damping rates obtained can be up to $h^{-1}$
times larger than those due to the resonant interaction with the disc, where
$h$ is the disc's aspect ratio. This suggests that models that incorporate
planet-disc interactions using well-known formulae based on resonant
wave-launching to describe the evolution of eccentricity and inclination
underestimate the damping action of the disc on the eccentricity and
inclination of low-mass planets by an order of magnitude.
