2001 cavalier overheating

I have a 2001 cavalier, the temp runs hot in no time at all, like to the red high
mostly when idling but does creep up at times, i will just start to drive and it
will slowly go down a bit but not to much, I replaced the relay switch because
that was not working, I checked all the fuses and they are good, the fan in
front does not work is there a way to test the fan without one of those meter
readers? I turned on the air conditioner and left it but the fan did not come on,
when i turn the heat on a bit to see if that will help ease the temperature it
seems to rise not lower,more problems later. I asked the guy who sold me the
car and he just laughed and said oh yah that one so no help from him. I need
to break down the problems, it also has a gurgle sound behind the dash
wondering if this could be related at all. no leaks from the car at all, no smoke
from tail pipe, nothing comes from the hood, starts up great drives good no
weird sounds or smells that I have noticed.