I've never heard of plain ol' heat causing problems. I live in Kansas. We can't match your humidity but it gets to 110+ in the summer. (Hot glue melts off the planes - I don't use it.)
LiPos will (sometimes) cause a fire if they are severely damaged (such that the inner cells are penetrated) or if they are overcharged or improperly charged. DO NOT use a charger not specifically designed for LiPos. Do not hit them with an axe. Other than that, they're pretty hard to make burn. They developed a bad rep early on when they were being charged on the wrong chargers in the wrong way.
You can get an explosion charging a car battery improperly.
Yes, there are a number of anecdotal stories about them starting fires and they can, but it's really, really rare with any kind of care.
Charging is the most 'dangerous' time and, as I said, you can always charge them in a special container
or just in a Pyrex pot.