That will be difficult.
If you want it cheap your best bet is a room in a shared appartment, let out by a student who is away for a semester abroad.
Check out this side: www.wg-gesucht.de
WG is a German abbreviation for a shared flat. Look for rooms available for Zwischenmiete, literally rent-in-between.
If your money resources are endless and you want something highclass, check out normal holiday appartments. The difficulty here will be finding something that is available for 3 months. Call the Tourist Information of Berlin for addresses. www.berlin.de