  Low-mass planets that are in the process of growing larger within
protoplanetary disks exchange torques with the disk and change their semi-major
axis accordingly. This process is called type I migration and is strongly
dependent on the underlying disk structure. As a result, there are many
uncertainties about planetary migration in general. In a number of simulations,
the current type I migration rates lead to planets reaching the inner edge of
the disk within the disk lifetime. A new kind of torque exchange between planet
and disk, the thermal torque, aims to slow down inward migration via the
heating torque. The heating torque may even cause planets to migrate outwards,
if the planetary luminosity is large enough. Here, we study the influence on
planetary migration of the thermal torque on top of previous type I models. We
find that the formula of Paardekooper et al. (2011) allows for more outward
migration than that of Jim\'enez & Masset (2017) in most configurations, but we
also find that planets evolve to very similar mass and final orbital radius
using both formulae in a single planet-formation scenario, including pebble and
gas accretion. Adding the thermal torque can introduce new, but small, regions
of outwards migration if the accretion rates onto the planet correspond to
typical solid accretion rates following the pebble accretion scenario. If the
accretion rates onto the planets become very large, as could be the case in
environments with large pebble fluxes (e.g., high-metallicity environments),
the thermal torque can allow more efficient outward migration. However, even
then, the changes for the final mass and orbital positions in our planet
formation scenario are quite small. This implies that for single planet
evolution scenarios, the influence of the heating torque is probably
negligible.
