We investigate the effects of radiative energy transfer on a series of nested-grid, high-resolution hydrodynamic simulations of gas and particle dynamics in the vicinity of an Earth-mass planetary embryo. We include heating due to the accretion of solids and the subsequent convective motions. Using a constant embryo surface temperature, we show that radiative energy transport results in a tendency to reduce the entropy in the primordial atmosphere, but this tendency is alleviated by an increase in the strength of convective energy transport, triggered by a correspondingly increased superadiabatic temperature gradient. As a consequence, the amplitude of the convective motions increase by roughly an order of magnitude in the vicinity of the embryo. In the cases investigated here, where the optical depth towards the disc surface is larger than unity, the reduction of the temperature in the outer parts of the Hill sphere relative to cases without radiative energy transport is only ∼100 K, while the mass density increase is of the order of a factor of two in the inner parts of the Hill sphere. Our results demonstrate that, unless unrealistically low dust opacities are assumed, radiative cooling in the context of primordial rocky planet atmospheres can only become important after the disc surface density has dropped significantly below minimum-mass-solar-nebula values.