  We calculate radial migration rates of protoplanets in laminar minimum mass
solar nebula discs using three-dimensional self-gravitating radiation
hydrodynamical (RHD) models. The protoplanets are free to migrate, whereupon
their migration rates are measured. For low mass protoplanets (10-50 M_\oplus)
we find increases in the migration timescales of up to an order of magnitude
between locally-isothermal and RHD models. In the high-mass regime the
migration rates are changed very little. These results are arrived at by
calculating migration rates in locally-isothermal models, before sequentially
introducing self-gravity, and radiative transfer, allowing us to isolate the
effects of the additional physics. We find that using a locally-isothermal
equation of state, without self-gravity, we reproduce the migration rates
obtained by previous analytic and numerical models. We explore the impact of
different protoplanet models, and changes to their assumed radii, upon
migration. The introduction of self-gravity gives a slight reduction of the
migration rates, whilst the inertial mass problem, which has been proposed for
high mass protoplanets with circumplanetary discs, is reproduced. Upon
introducing radiative transfer to models of low mass protoplanets (\approx 10
M_\oplus), modelled as small radius accreting point masses, we find outward
migration with a rate of approximately twice the analytic inward rate. However,
when modelling such a protoplanet in a more realistic manner, with a surface
which enables the formation of a deep envelope, this outward migration is not
seen.
