Just quick,

If my CPU is overheating would that effect gameplay in CSS dramatically?

(Speedfan shows my CPU goes to 60 degrees when i play css.)

it the computer still works its not overheating...

that is probably your main problem.. your choice of words
"running hot" would have been my choice. and no. i dont think it would affect how you play CS.. however. some people seem to like cpu overheat protection applications.. some of which shut the computer down or force the cpu to run at a slower speed. these actions result in a lower core temperature and save your cpu from certain death.

that said.. ive had my cpus running at 60C and higher 24/7 for over a year.. (they run a bit colder now)