The answer is, that first of all there is no difference between doing a melocho for a jew or for a non jew.
Now, this is a classic case of a sugya called chazara.
In order to be able to return something to its heat source, you need 3 conditions that are known as "Tenoi Chazara".
They are, that the pot must still be in your hand, AND that you had intent to return it to the heat source, AND that you didnt put it on the ground.
ALSO the heat source must be "Garuf V'katom", which means that the coals are either covered with dirt or swept out of the oven, to make sure that you wont stoke the coals.
Now regarding our electrical appliances nowadays, you must have the heat source covered. The most practical cover is to line the crock pot with silver foil.
Regarding sfardim, R' Ovadia Yosef held that a hot plate is intrinsically Garuf V'katum. But i dont know if he held the same for a crock pot. Could be yes, i just dont know.
ALSO, all these things are issurei d'rabbonon. BUT YOU CANNOT FORGET ABOUT THE ISSUREI D'ORAYSA'S
Meaning that if the oatmeal is liquidy, and it cooled down, you MAY NOT put it back because that is going to be "bishul acher bishul on a liquid".
All that was in regards to putting it back, assuming that you were allowed to eat it to begin with. Now comes the problem of Amira L'akum.
If the non jew cooked it for you, then you were not allowed to eat it to begin with.
If it was cooked for the non jews, then you have to take into account how many jews were there, because if he added any for the jews, that is problematic