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For longer rentals, you could check Ebay Kleinanzeigen or Immoscout24 (the latter mostly for realtor ads) or WG-gesucht for shared places.
But for just a few months (and presumably furnished), your options there are probably severely limited. So you better also check short-term serviced apartments (which cost the same as cheap hotels or B&Bs, but are more suited to your situation).

tbous wrote:

Hello!

  I'm a US professor of art coming to Berlin to do a project with the Museum für Naturkunde. I need a place to sleep. Ideally that would be in a live/work space where I could also to make some lightweight assemblage. I'm coming from September 1 through December 15th. I lived in Berlin off and on in the 2000's, speak some German, and am open to a shared situation.

I can't help you with specific advice about Berlin. But what I know is that it has drastically changed.  It was once a place of cheap apartments and lots of spaces for artists. Then then the gentrification and property sharks moved in. Places that were very cheap are now luxury condos. Berlin is a big place so I am sure there are still possibilities but the availability and cost of places where one might have an apartment/studio arrangement are drastically reduced. Good luck.