I've spent quite a bit of time in the Kalimantan provinces in southern Borneo. I've only shot black and white, but I did wish for colour for the wild flowers. Most of the photo opportunities I had were where there were openings in the forest, like along rivers and roads, and where there were villages. Almost all the wildlife I've seen were on the margins of the jungle. Once deep inside the forest there was very little in the way of wildlife of any kind, even bugs. I've never been to Sarawak or Sabah, but hopefully they have more natural forest remaining than does Peninsular Malaysia. When you are in the forest itself it is not as hot as in the open areas, and not unpleasant.
I couldn't carry a lot of camera gear in addition to my working gear, so I took one 35mm camera and two zooms, covering 28 to 300mm. And lots of HP5+. A tripod or at least a monopod would be very useful inside the forest.
I'm sure you already know this, but don't forget some ziplock bags to put the cameras/lenses in before going from the hot humid outside into an air-conditioned room.