When was the last time you changed the timing belt?
Mine does this too every morning, but only right after being started and not allowed to warm up first.
My timing belt is one tooth too far advanced and my problem started then I replaced my timing belt.
I need to reset my timing belt.
Your belt might be stretched and needing to be replaced.
If you have not changed it, it is recommended to change it every 60,000 miles.
You could take it to a shop that has a ÔÇ£dinoÔÇØ and have them check the timing while under load to see if they can see if the timing is too advanced and is causing the problem.
If your KIA is an automatic, it might be going into ÔÇ£limpÔÇØ mode after experiencing this problem and letting it sit for 10 min might be letting it reset.

Good luck and let us know what you find out.
Logansportage