Have been living and biking in Singapore for over five years now, and around Asia for longer. Lightwieght XC kit is the way to go, but honestly – no matter what you will be hot, sweaty and miserable – especially if you are just arriving from somewhere cool like the UK. As @jambalaya said – there’s a lot of night riding, just to avoid at least the worst of the heat. Plus you get to see some very interesting animals in the jungle at night!
The heat is there, you just have to get used to it, and there is no magic kit solution that will make you comfortable when you are in a jungle at 33 degrees C and nearly 100% humidity. The things you should be wary of are sunscreen (mainly if you are on the road), mosquitos (dengue fever is a big issue in most of SE Asia, and malaria in parts), and hydration.
ironically a big problem for me is when I’m out riding and a heavy rain starts; for the first 20 minutes or so it can be really refreshing, but after that it actually gets quite cold – and I _never_ have anything additional to wear with me…