  We investigate by means of numerical simulations with nested Cartesian meshes
the force exerted on a massive and luminous perturber moving at constant speed
through a homogeneous and opaque gas, taking into account thermal diffusion in
the gas and the radiative feedback from the perturber. The force arising from
the release of energy into the ambient medium by the perturber, or heating
force, is directed along the direction of motion and induces an acceleration of
the perturber. Its value is compared to analytic estimates in the low and high
Mach number limits, and found to match those accurately. In addition, the drag
exerted on a non-luminous perturber significantly departs from the adiabatic
expression when thermal diffusion is taken into account. In the limit of a
vanishing velocity, this drag tends to a finite value which we determine using
linear perturbation theory and corroborate with numerical simulations. The drag
on a non-luminous perturber in a non-adiabatic gas therefore behaves like dry
or solid friction. We work out the luminosity threshold to get a net
acceleration of the perturber and find it to be generally much smaller than the
luminosity of accreting low-mass planetary embryos embedded in a gaseous
protoplanetary disc at a few astronomical units. We also present in some detail
our implementation of nested meshes, which runs in parallel over several
\emph{Graphics Processing Units} (GPUs).
