The best time to visit Gili T is between May and October, which is the island's dry season. Keep in mind, this also means that it will be the busiest time of year to visit the Gilis. Peak tourist season is from mid-June to early September. My advice is to visit in the shoulder season to get decent weather but avoid the crowds.  The Gili Islands are located very close to the equator, so the climate is very warm and tropical. Temperatures vary in the dry vs. wet season, but typically the island's temperature is around 80 degrees Fahrenheit.