Your auxiliary fan, supposing its still in optimal working condition, should be fine. If it shuts off too soon, then you'd notice your engine temp to spike as well. This is assuming your condenser is in front of your radiator.

But since its crank driven, your issues migrate to something more along the A/C's subsystems.

The problem in those situations normally have more to do with your refrigerant levels. If after a full charge and this is still a problem the A/C's internals may need to get some work done.