Weather in Göttingen
Typically, the weather in late June in Göttingen is quite enjoyable.
But you never know, so be prepared to check the weather before you come here and bring an umbrella. For example, last year in 2017 in the last week of June we had about 24 C and occasional showers. Sometimes the nights can be chilly, even in June.
One good and usually reliable weather forecast can be found here. It is in German, but it should be self-explanatory. Of course, there are many more resources.