The main rainy season lasts from the end of March through to mid-June, however it is hard to predict precisely when it starts and ends. It's the warmest time of the year in Tanzania, but those months are so wet that many operators simply do not offer climbs in April/May.
The rain gradually decreases, and so do the temperatures on Kilimanjaro. The weather on Kilimanjaro is fairly dry and clear, but the nights are bitter cold. The number of climbers in June are few, but the number increases as the year progresses.