I have a 2000 cavalier that has acquired this problem 2 years ago and had to install a separate cooling fan control to fix it. People who try to talk us down as if we are dumb by stating that the cooling fan is actually suppose to turn on at around 226-230F is full of crap. That may be true for the actual engine coolant temp, but I believe that it has always actually came on at 200-210F because of the computer responding to transmission temperatures (which is the temperature that ALWAYS signals the computer to turn on the cooling fan on ALL Cavaliers). I believe this because weeks after my cooling fan stopped turning on for these temperatures suddenly the transmission began messing up as the tranny runs hotter than normal. Fluid slowly burning needing to be changed every 4 months. Then suddenly in the mid summer the transmission throws P1870 engine codes. 2 weeks later the tranny overheats and dies with the cooling fan (turning on too late) staying on trying to cool the transmission down. This led me to believe that the tranny has it's own sensor that also triggers the fan as the engine coolant temp was at about 185F at the time. Also on cold starts the fan always turned on ONCE when warmed up to 200F and stayed on for 10 minutes without stopping then never turns on again until at about 230F due to the engine coolant temp trigger. Tranny overheats a couple times until I installed a separate cooling fan control that turns the fan on at about 210F. Since then it has never overheated again, but the damage was done and the tranny held on for about 7 more months before shifts of gears and reverse became a problem. So I replaced the tranny myself and still never overheated. I had a hunch so I decided the remove the new cooling fan control connections and reconnect the original ones for full computer control. What I found was the car working perfectly again turning on the cooling fan at around 200-210F with the NEW transmission all by itself.
I also can't stand when people say the problem is the coolant switch as these Cavaliers DO NOT have cooling fan switches. It is the computer itself that controls when to turn on the fan as it reads data fron the coolant temperature sensor. It's also irritating to see people telling others to change the temp sensor. Here's a tip, if you are able to read the temp on the dashboard then so can your computer, meaning the sensor is working perfectly.
Source: I am a 10 year mechanic and this is from personal experiece from my own vehicle.