Folks in humid, hot climates - what do you do to cool your house down at night?

I'm sitting here on a cool beautiful morning - it's 65 deg F out, but it's 77 and stuffy inside my house. The air conditioner ran all afternoon yesterday, got to set sometime in the evening, and then the house hasn't dropped a single degree all night. Why not open the windows up, you say? It 98% humidity out. It's like this every day. I've had mildew on everything I own before. Never again. Has anybody else living in a temperate near-jungle climate figured out what to do about this? How does my house hold so much heat? Does an attic fan help? Any ideas???