  Using linear perturbation theory, we evaluate the time-dependent force
exerted on an eccentric and inclined low-mass planet embedded in a gaseous
protoplanetary disc with finite thermal diffusivity $\chi$. We assume the
eccentricity and inclination to be small compared to the size of the thermal
lobes $\lambda\sim(\chi/\Omega)^{1/2}$, itself generally much smaller than the
scalelength of pressure $H$. When the planet is non-luminous, we find that its
eccentricity and inclination are vigorously damped by the disc, over a
timescale shorter by a factor $H/\lambda$ than the damping timescale in
adiabatic discs. On the contrary, when the luminosity-to-mass ratio of the
planet exceeds a threshold that depends on the disc's properties, its
eccentricity and inclination undergo an exponential growth. In the limit of a
large luminosity, the growth rate of the eccentricity is 2.5~times larger than
that of the inclination, in agreement with previous numerical work. Depending
on their luminosity, planetary embryos therefore exhibit much more diverse
behaviours than the mild damping of eccentricity and inclination considered
hitherto.
