Autumn holds three months that barely resemble each other, so the gap between them matters more than any average. September still feels like summer, November feels like winter, and October is the hinge between the two.
September
Highs sit near 17-19 °C across the country, warm enough for a jacket-free afternoon and cool enough to walk all day. Berlin runs 15-20 °C, or 59-68 °F, and Munich sits between 10 °C and 20 °C.
Munich owns the month, because Oktoberfest on the Theresienwiese starts in September and runs into early October. It pulls visitors from everywhere, so a Munich tour booked for that week is worth arranging months ahead. Down the Moselle valley the wine harvest brings its own festivals, quieter ones where a glass and a free afternoon are the whole plan.
The festival crowd leaves with the first days of October. After that the Residenz, the Pinakothek museums and the historic churches in Munich are easier to walk into, and the city goes back to its normal rhythm.

October
By October the highs drop to around 12-13 °C or lower, the nights get cold, and rain becomes more likely, especially this month, with fog and flat gray skies moving in behind it.
Space is what you get back. Heidelberg and Nuremberg thin out as the peak crowds fade, the forests in the Harz and Saxon Switzerland turn gold and red, and Neuschwanstein looks better in the softer light. Berlin shows the same shift in the Tiergarten and the gardens at Schloss Charlottenburg. In Düsseldorf the Königsallee is worth an early-evening walk in this light, and in Munich the English Garden and the paths along the Isar turn gold. A Germany tour in October trades the crowds for the color.
November
Crowds thin out and the light goes early. Berlin drops to about 7-10 °C, or 45-50 °F, and the daylight shortens through the month, so an afternoon walk can end in the dark before you expect it.
That is a fair trade if you like being indoors. The autumn program of art exhibitions, theater premieres and music runs through the month in Berlin, and the museums are calm enough to take your time in. In Munich the markets and stalls run from mid-November through December, which gives you the lit stalls without the December crowds.