  We study the evolution of the eccentricity and inclination of protoplanetary
embryos and low-mass protoplanets (from a fraction of an Earth mass to a few
Earth masses) embedded in a protoplanetary disc, by means of three dimensional
hydrodynamics calculations with radiative transfer in the diffusion limit. When
the protoplanets radiate in the surrounding disc the energy released by the
accretion of solids, their eccentricity and inclination experience a growth
toward values which depend on the luminosity to mass ratio of the planet, which
are comparable to the disc's aspect ratio and which are reached over timescales
of a few thousand years. This growth is triggered by the appearance of a hot,
under-dense region in the vicinity of the planet. The growth rate of the
eccentricity is typically three times larger than that of the inclination. In
long term calculations, we find that the excitation of eccentricity and the
excitation of inclination are not independent. In the particular case in which
a planet has initially a very small eccentricity and inclination, the
eccentricity largely overruns the inclination. When the eccentricity reaches
its asymptotic value, the growth of inclination is quenched, yielding an
eccentric orbit with a very low inclination. As a side result, we find that the
eccentricity and inclination of non-luminous planets are damped more vigorously
in radiative discs than in isothermal discs.
