Look into the AMD Radeon R9 270X, that thing is a BEAST and extremely competitive around the ~$250 mark
I'd suggest an MSi-built card, my Cyclone GTX-550Ti has ran beautifully for 2 years under intense usage
However it sounds like the cooling in your case isn't optimal. What manufacturer is your GTX-560? That card shouldn't be operating that hot under any circumstances; I'd suggest rearranging some things and getting better fans.
EDIT: stuff. Read that as 100 Celsius.