  We perform three-dimensional self-gravitating radiative transfer simulations
of protoplanet migration in circumstellar discs to explore the impact upon
migration of the radial temperature profiles in these discs. We model
protoplanets with masses ranging between 10-100 M\bigoplus, in discs with
surface density profiles of {\Sigma} \varpropto r^-1/2, and temperature
profiles of the form T \varpropto r^-{\beta}, where {\beta} ranges 0-2. We find
that steep ({\beta} > 1) temperature profiles lead to outward migration of low
mass protoplanets in interstellar grain opacity discs, but in more optically
thin discs the migration is always inwards. The trend in migration rates with
changing {\beta} obtained from our models shows good agreement with those
obtained using recent analytic descriptions which include consideration of the
co-orbital torques and their saturation. We find that switching between two
models of the protoplanet, one in which accretion acts by evacuating gas and
one in which gas piles up on a surface to form an atmosphere, leads to a small
shift in the migration rates. If comparing these models in discs with
conditions which lead to a marginally inward migration, the small shift can
lead to outward migration. However, the direction and speed of migration is
dominated by disc conditions rather than by the specific prescription used to
model the flow near the protoplanet.
