Try some Lucas transmission medic. Also make sure that you have the correct weight oil. The warm tells me that as the oil lube thins down it circulates fine. Adjust to a lighter weight oil.
It sounds like a vacuum problem is keeping the EGR valve open causing the other sensors to read this and more fuel would be injected by the ECM. u may of gotten an egr code but the problem is not the valve itself.
No promises but this is the only reference I could find for Hyundai where the fuse box was not behind a panel to the bottom side of steering wheel. It may inspire you to look elsewhere behind items. Good Luck.
"The interior fuse panel is located behind the coin holder pull out drawer, which is on the lower left side of the dashboard"
it sounds like the oil sending unit which is an inexpensive part and simple to replace it should be located between radiator and engine on the side of the oil pan