What about exchanging out the bathroom vent fan for a Fantastic Fan? It can run off your trailer battery when there are no hook ups. Most Fantastic Fan models are reversable so you can remove the warmer air or bring in cooler air.
I did this and was worth the investment. The bathroom is on the other end of the trailer from the bed.
But got to say that I haven't ran the Fantastic Fan much without hook ups so someone else will need to add their two cents on this suggestion.
Also keep in mind the heat issue is more of a problem during the hotter months.
Great choice for "Living within my means" and camping for one...
2011 Salem Cruise Lite 20RBXL & 2011 Toyota Tundra Dbl Cab
Camping History: 45 Trips / 133 Nights / 3736 Miles
FRF Social Group: Campers of the West