A cold start start engine will rin about 5min, than will start running rought and shut down. will not restart till it cools down

Make,year,model,engine? don-ohio

check your fuel filter and spay your carb with cleaner

Might have to reset the codes on the computer. Take the + battery cable off the battery and reconnect it afer 5 minutes. Next try to start the engine without holding the gas petal down, it should start and run rought till the computer resets itself. If engine stops, restart the engine and hold the gas petal down and give it enought gas so it will run smooth, it may take 5 minutes or so for it to smooth out and run at idle speed. If this did not fix the problem, check for a vaccum hose that may be off some where on the engine

sounds like your auto choke is stuck on had the same problem with a honda i worked on would be fine untill got to running temp then would run like **** and stall out and wouldnt start again till cold

I know this sounds silly but Replace the crankshaft position sensor. My guess is it will start shutting itself off soon and restarting when it cools off. I think its just giving you a warning lol.

replace the ignition control module.

check your relays relays can build to much resistance and overheat and they shut down then they cool down and there good till they get hot again
and they dont usually set a check engine light

Living in Thailand I had a lot of stalling problems. It started with my engine not running smooth when driving away cold. After half a km or so the car would just die or after even a longer distance stalling at full speed. Restarting worked and mostly I could drive on. Sometimes it would stall in a traffic jam.

Checked everything, but could not really put 1 and 1 together until I noticed that I was loosing a little cooling liquid and kept refilling on a regular basis. Found that every time this problem occurred also the cooling liquid was low again. Refilling the liquid solved the problem till the cooling liquid/water was low again. After fixing the actual leaking hose the problem disapeared totally. Later when my radiator started leaking slightly the problem came back as before. Now the car is fitted with a new radiator no problems like this anymore for more then 1 year.
I think the engine management system of the KIA is very sensitive for low water and maybe the temperature changes coming with it.

Maybe worth checking?

check and see if you get water/coolant circulates when you have the cap off (only check from cold start) the original water pump came with a plastic impeller and tends to strip on the shaft also check your thermostat before replacing water pump.

done the same in my volvo it was disrubitor but make certain that replacement one the same part number.