Most all tractors and all Kubotas use the transmission case for the reservoir for hydraulics as well as the splash lube for the transmission.
If the heat problem is what you are after, check to be sure the three point hitch is coming off high pressure - neutrallizing at the top of travel.
This is easy to do - with the engine dead and the hitch arms empty, grab one of the lower arms and lift it to the top of travel. Make a mark with a piece of chalk or magic marker on the arm and top cover - a straight horizontal line when you feel the bellcrank under the top cover hit the stop.
Then get on the tractor - start it and pull the position control handle fully back and see if the arms travel to the top. The mark you just made should not be lined up but should be offset / staggered. If the mark lines up, find the external linkage (on one side of the rockshaft externally) and extend the linkage until such time that the line is offset / staggered.
This means the position control valve is fully seated and neutralized. If it is not, the pump is constantly blowing the relief and that makes heat in the system.
If you want to verify the symptom, shorten the linkage and listen to the engine load up - when you lengthen it, you will hear the engine RPM change.
This also will make your loader not have as much power to lift with the hitch fully raised. Very common issue because people mess with the linkage to get more lift height. Just as easy to fix, if this is the source of the heat.
Good luck!
YC