The check engine light indicates a stored code in the ECU, or engine computer, what you can do is, go to Autozone, or maybe Advance Auto, lots of auto parts stores have this service. Ask them to scan the codes, all cars made after 1996 in USA are required a diagnostic port, and the port reports back what the sensors in the car are saying, and if the sensors readings aren't in parameters, you get the check engine light. So your first task would be to go find out what exactly the codes are saying.
Also, you DON'T need a thermostat unless your car will not heat up. By heat up, generally your temperature gauge should go to the middle, or close to it, and stay there, and do this in a reasonable amount of time (10 minutes or so of driving.) Or, conversely, if your car is overheating, then you also need a thermostat. For future reference, you can tell if it's the thermostat making the car overheat if your car's water temp gauge goes all the way high within a short time of startup, and then in a few minutes drops back down to the middle, that means the thermostat is stuck closed, or delayed opening.
If you want to make the codes go away, you can disconnect the battery cables from your car for a little bit, some cars it's as little as 30 seconds, some cars as much as an hour or two. However, this won't actually fix the issue of what's making the codes go, but if it was a temporary thing (ie, bad gasoline or air cleaner being dirty or something) that triggered the codes, then it'll get the light off your dash. Also, at Autozone when you get the codes checked, you can get their machine to clear the ECU of codes, too, but if the ECU throws new codes again, then yes.
Anyway, I've probably overwhelmed you with information. The short answer is take it to an auto parts store and get what the actual codes it's throwing are. Then work from there. Hopefully it's something simple, like a bad air filter, bad plug wires, some random sensor is bad, and not anything disastrous like a headgasket, but good luck.