Bathroom ventilation and cooling

I have a full bath off of the master bedroom that is on the east side of the house. It has an HVAC vent, but vent to remove moisture. There is a small window as well. The problem is the room gets too hot in the mornings and the better half says she can not do her hair and what not.

The two ideas I have are to add a vent and fan for the humidity and change the lighting to some bulbs that put out less heat. Are there any other ideas on ways to keep the room cooler?

We keep the AC running pretty cool thru the night, that room just seems to warm up quickly.

Thanks