I've taken some sticks to the Dominican with me a few times and never had the same problem. The humidity almost isn't a concern - it's pretty humid there year-round and I find a double-baggie solution more than enough (of course, I'm never there for more than a week at a time).

I don't think the warmth should be a major concern as far as beetles go, unless your stay is extended. Best advice if you're worried about that is freezing the sticks you're planning to bring. I know some people don't like to freeze, but if you're really worried about it, that'll set your mind at ease.