Early September can still be quite hot, but generally not as bad as July-Aug. Northern Japan or higher altitudes (e.g. Hakone / Nikko) will be cooler. There's no significant difference in rainfall between northern Japan and Tokyo at that time of year. (The rain divide is along the center of the country - with the Sea of Japan coast getting more much more rain than the Pacific coast). If anything, the further north you go, the less likely you are to encounter a typhoon, which can hit at that time of year - usually approaching Japan from the south / west.