Why would they assume a solid body? It is well known that the rotational period of the solar polar regions does not match the equator. That’s why we get sunspots — the magnetic field lines twist and tear due to differential rotation.
Of course, if the star is “squashed” with a “distended” equator, then of course the poles are warmer — they are closer to the nuclear core that powers the star.
Never fear, Captain Kirk and his crew will sort it out in a few centuries. ;’)