Search for rooms if you cannot afford appartment.
Good advice. I don't think he'll find a short term apartment for much less than 2500zl - in fact that is not expensive.
One leftfield solution is the hall of residence for the Music Academy which lets rooms outside term time. It's in a beautiful Eighteenth Century building just off the Rynek. There are other university halls available to visitors in summer of course however I have stayed at that one and recommend it.