A lot of Deere stuff over the years has two thermostats. If one of the sticks shut the tractor will operate normally up to about half load. Anything over that and not enough water can get through the one thermostat that is still working and opening up. Any more load and it will run warm or hot. We had a 4020 that did that. Ran fine in the winter but come spring warm up would start running hot under heavy load. Light load was perfect. Had one thermostat stuck shut. Also had a 3020 that a thermostat stuck shut. They only have one (identical to the two that are in 4020's). It got hot in a hurry and it didn't matter what kind of a load was on it.

If it has two thermostats, have them checked, one may be stuck shut.

John