3 Months Stay in Cologne, GERMANY

Finding a furnished place for 3 months on the open market will be difficult and expensive. The best chance is a room in a shared apartment or WG in German. These are common for students and young people and one will normally find rooms advertised at any University. There are usually certain places where there are pin-boards for such things. But you will probably have to have a hotel or hostel to begin with since it is not so likely people will agree to give a room until they have met you personally. Students leave or go away for a semester and are happy to rent out their room for a limited time period. The question might be more of location and finding the fitting people. Availability probably varies a lot. I think the end/beginning  of a semester has a lot of turnover but by the middle of a semester it is much harder. Doesn't fit to be quiet and studious and then live with a bunch of young people partying all of the time or vice versa. If one doesn't find a furnished place, one can get the basics at Ikea or second hand and sell or give them away when you leave. This will still be cheaper than finding your own furnished apartment.