the auto brake is not trying to steer the aircraft as far as I know
Correct.
Autobrake simply applies equal pressure to both sides in order to achieve a set deceleration rate. A slipping wheel will be detected by the anti skid unit and its individual brake pressure will be reduced until the wheel spins up to speed again.
If the weight load of the aircraft is not evenly balanced due to the crosswind effect, then the upwind wheels will have less load on them, tend to start to skid earlier which will cause the antiskid units to reduce brake pressure on those wheels.
Thus the downwind brakes work harder and show it as an increase in temperature.