I made this account for my grandfather to ask for help with a problem with his car. He has a 2001 Accent and basically it will die while idling if the RPM drops too low and not want to start back up until it has cooled down or unless you use starter fluid. He thinks it could be the idling sensor or the connection to the idling sensor. Here is what he transcribed for me to relay to you:

Starts cold and warms up to temp at idle. Then after 8 to 10 minutes the motor stops and will not start until it cools down. Then it will start up and run for 2 to 3 minutes and stop again unless kept running at higher RPMs.

Cleaned idle control valve.
The check engine light does not come on.

3:15 Started motor, 1200 RPM, Ran up to temp
3:20 900 RPM in drive
3:22 1200 RPM Motor fans came on
3:27 RPM surges above 2000 RPM
3:29 Back at 1200 idle, temp normal
3:30 RPM goes up and then down
3:40 Stopped motor then restarted, 1200 RPM, temp normal, Stopped motor
4:45 Motor would not start
5:50 Motor started, idle at 1000 then went to 900, temp normal, ran steady at 2500 rpm
5:55 RPM started to go up and then down + or - ~500 RPM, but continued to run. Stopped the motor
6:43 Started motor, ran steady at 1000 RPM for 2 mins then went from 1000 to 800, then back to 1000, ran for 4 or 5 minutes then stopped motor.
7:00 Motor would not start