I have a Honda Civic LX 2002 and I'm having issues with my car overheating

I have a Honda Civic LX 2002 and I'm having issues with my car overheating. My temperature gauge fluctuates, when I'm at a complete stop my car will start to overheat but once I accelerate my car starts to cool down. Now, my first instinct was to change the thermostat, which I did but it's still giving me the same issues. I have check to see if the radiator or any of the hoses were leaking because everytime i drive i have to add coolant to the raditor but nothing, nothing leaks out. I don't know where to go from here, and I'm getting tired of adding coolant to the radiator every single time I have to drive. Any suggestions?

Bad water pump.

The cooling fans are not working.

What you have described is classic cooling fan failure. If a fan is not properly functioning your car will over heat at idle or low speeds. The issue disappears at higher speeds due to the natural intake of air which occurs when in motion.

Replace the bad headgasket.

Honda civics model 2001 - 2005 are known to have overheating problems due to a bad headgasket. The leak may be small, but there's coolant loss in the affected cylinder. Sometimes, this problem is accompanied by a misfire code caused on initial starts, and it is more recurrent after driving and letting the car sit for a while.
If you want to know for sure that this is the problem, do a leak down test on all cylinders.

Your losing coolant at a prodigious rate but its not leaking?

WRONG.

Obviously there's a leak. Its a closed system. If you have to add then it is being subtracted from somewhere. Stop being cheap and go to a proper mechanic.