Sitting on the equator, Indonesia experiences a warm, balmy tropical climate. With temperatures hovering between 27 and 30 degrees throughout the year, the only consideration is rainfall.
Indonesia's driest period falls between April and October, with July and August considered the 'peak season' for beach resorts in Bali, Lombok, Java, and most other places. The only exceptions to this rule are the jungle/rainforest regions of Sumatra, Kalimantan, and Sulawesi, which may receive a daily downpour, albeit passing quickly.
Humidity levels can vary from the coastal regions to the Hinterlands, so do bear in mind where you choose t spend the bulk of your time. The only properly cold places in Indonesia are the very tops of the high peaks, where temperatures may plunge to near freezing before sunrise, which means you may need to carry warm clothing if trekking in hills or ascending volcanoes early morning!
Travelling to Indonesia out of season can be advantageous, as temperatures remain constant despite the rainfall but accommodation prices fall significantly. However, this is not recommended for wildlife explorations, as some National parks and resorts may be inaccessible due to rising water levels.