My 2004 Hyundai accent runs hot I replaced my thermostat but still running hot dont need water it's full and it might be parked all day but as soon as I start driven it starts to run hot

2004? Check the coolant, water pump, thermostat, plug up the radiator.

Both cooling fans should run continuous when A/C is on. Switch A/C off to avoid Blown head gasket hazard.

Water pump?

Most likely the thermostat broke. I expect that you have an older Hyundai and never had the anti-freeze changed. When the engine is cold the thermostat is closed which causes the engine to warm up more quickly. A warm engine runs more efficiently (less gas) and more smoothly. When the engine temp reaches a certain temp the thermostat opens and then allows the hot engine coolant to run through the lines to the heater core. The heater blows air over the heater core which produces the warm air that warms up the cabin. Thermostats used to be cheap and easy to change. I would suggest a web search for how to replace the thermostat. Something like 'hyundai accent 2002 replace thermostat".

check your thermostat if its block it can get hot .start your car make it really hot and check the bottom hose and the top hose of the radiator if its different temp. your thermostat needs replacing

not sure here without getting it hot and running my hands over the rad to see if its hot around the edges and cool in the centre where the fan is as this will signify a chocked up radiator but if its cooling with the heater on full blow then i would suspect a cooling fan fault ,as a water pump plastic impeller fault would not push the water through the heater matrix ,Also i dont think this vehicle has the plastic impeller but a metal one if my memory serves me correctly ,check the cooling fan electrics as iam sure this is a temperature switch fault

Look for air bleeds, sounds like the coolant has air pockets. And ALWAYS check coolent level with heater set to full heat, or water valves would be closed, and blocking coolant...

My 2000 accent will stall only when hot and will not start till it cools down.

replace the battery hyundai/kia use some pretty crappy batteries i am a kia / hyundai tech and have had to replace batteries when the cars have come off the truck i would buy an interstae or exide and you wont ahve the issue again

If the water tends to keep going down then there has to be a leak somewhere. Try also looking at the hose coming from the overflow tank and see if the hose might be kinked. You might also be blowing antifreeze out the tailpipe. Take a look and if there is bluish white smoke then you have confirmed that theory,