You didn't ask about bus routes for the place at Governor & Market, but I'll tell you in case you don't know, in addition to the N. Dodge route, there is the Free Shuttle that would take you to campus if you are willing to walk 4 blocks to Johnson & Bloomington. Just another option to consider.
At E. Court and Muscatine, I'd guess the Court Hill bus would be your best bet. I know there is a stop at Summit & Burlington, which is not too far away, and there might be one even closer. I can't find a list of IC bus stops anywhere. Here is the IC Transit website with route maps and times:
Transit - Bus Schedules
There is a IC Transit tripmaker here, which would have more details on stops but is not instant:
Transit - Tripmaker
As for the air conditioning, my sister lived in an old house downtown with window air conditioners and she made it. It might be warm sometimes, but it is doable. Many older homes downtown don't have central air conditioning because they are simply too old.