In Kenya and Tanzania climate has as much to do with altitude as with seasonality. With the equatorial and sub-equatorial situations, the Southern Hemisphere’s “reversed” seasons are in effect: winter falls in July; January is the height of summer.
In both countries the coast is warmer and more humid. If you’re traveling in the higher elevations (Highlands in Kenya and Ngorongoro in Tanzania) definitely bring a sweater and/or jacket no matter what the season…but especially during the late June through August cold period.