I can't help you with a suggestion for AC, but if you want to go to the mainland for a couple days I know just the place.
The Maruba jungle spa was so intoxicatingly sexy. Lush jungle atmosphere, red hibiscus flowers everywhere, throbbing music, etc.etc.etc.
We went horseback riding in the jungle, took a riverboat ride to the ruins at Lamanai, had meals of wild game, soaked in the hot mineral bath (nude at night), and had the most incredible full body massage with their famous Mood Mud.
I know people take day trips to Lamanai from San Pedro and stop at Maruba, so getting there should be no problem.