  We study the torque on low-mass planets embedded in protoplanetary discs in
the two-dimensional approximation, incorporating non-isothermal effects. We
couple linear estimates of the Lindblad (or wave) torque to a simple, but
non-linear, model of adiabatic corotation torques (or horseshoe drag),
resulting in a simple formula that governs Type I migration in non-isothermal
discs. This formula should apply in optically thick regions of the disc, where
viscous and thermal diffusion act to keep the horseshoe drag unsaturated. We
check this formula against numerical hydrodynamical simulations, using three
independent numerical methods, and find good agreement.
