Basically, it's a huge pain and you'll pay the landlord well to have a furnished apartment in the city for a short term lease. I did an away at Northwestern and lived downtown on the north side, and it was pretty expensive. The short term part really jacks up the rent - I think I paid $1600/mo for a 300sqft furnished studio. My apartment hunt was relatively last-minute, however, so if you RENT EARLY and stay out of the Near North/Gold Coast area, things can get substantially cheaper.
The company I used was sublet smart (
www.subletsmart.com), and aside from the price, the apartment was fine and the management was pretty good. I had some plumbing overflow problems and they came by several times afterwards to make sure everything was working.
The other place I remember was a set of apartments near the UIC/Rush/Stroger district specifically for medical professionals. I think it was medbeds (http://www.beds4meds.com/) but my friend who stayed there isn't sure. She did say the apartments were fine though.
I hope that helps. They may give you a better rate if you're staying for 3 months.
