2001 F150 won’t stay running

The vehicle should idle at a higher speed until it reaches operating temp, especially in cold weather. Check your idle on cold mornings. My 2010 idles about 500 RPM's higher until it warms up.

Gasoline vaporizes easier in warm weather than in cold. To compensate, the idle increases to deliver more gas during cold weather startup. If the idle settles back to normal after warm- up, there is nothing wrong.