Being equatorial, the temperatures on Kilimanjaro from one month to the next do not vary substantially on the mountain as they do e.g at the base. However, Tanzania does have two wet seasons.
The first is the long rains which normally run from March through to May, and then a short rainy season in November, which sometimes extends into the afternoons in the early days of December. Although you can get a discount to trek in the rainy season, it is best to go when the weather is warmer and more stable as rain brings with it mud, wet conditions and of course, snow.
The daytime temperatures tend to range around 32 to 38 degrees C in the forest, to anything from -2 to 6 degrees at the summit. Nights tend to range from 10 degrees down to well below freezing. Summit temperatures can drop below -20C. A general rule of thumb is that with every 200 metres in altitude climbed; the temperatures drop by a degree. Distances trekked per day will vary, between 6km’s on day two, to close on 30km’s on the day of your summit, dependent on which route you take.
The warmest months with the clearest trekking days on Kilimanjaro, are from mid to late December, January, February, September and October. The rains often come in April and the start of May with the possibility of some snow. June through to August are superb trekking months, though evening temperatures tend to be colder. The wettest months on Kilimanjaro are November and early December, where snowfalls are likely. Note, that as this is a mountain it is not impossible to get sporadic snow or rainfall at odd times throughout the year, although the snow normally only falls above 4800m.