  Rapidly rotating fluids have a rotation profile which depends only on the
distance from the rotation axis, in accordance with the Taylor-Proudman
theorem. Although the Sun was expected to be such a body, helioseismology
showed that the rotation rate in the convection zone is closer to constant on
radii. It has been postulated that this deviation is due to the poles being
warmer than the equator by a few degrees. Using numerical simulations, we show
that the pole-to-equator temperature difference cannot exceed 7 Kelvin as a
result of the back-reaction of the high-latitude baroclinically unstable
inertial modes. The observed amplitudes of the modes further indicate that this
maximum temperature difference is reached in the Sun. We conclude that the
Sun's latitudinal differential rotation reaches its maximum allowed value.
