it isn’t possibly locked is it? If it were locked, like the center diff in an AWD when you go into mode, if would cause a lot of gear loading on a hard surface, do not use mode/4wd on hard surfaces…
when you select mode the TCU powers a air solenoid valve under the passenger dash next to the fan solenoid, to send air to lockup that power divider axle diff. When you de-select mode, this solenoid valve should vent that lockup air. If that valve were leaking, that would apply air and keep that power divider locked Which would explain the heat/load as a locked divider would not allow any escape of torque due to wheel rpm differences…
Test 1: disconnect the air line to the power divider axle. Any air come out of it? shouldn’t be any when not in mode.
Test 2; jack up a rear wheel. If the power divider isn’t locked, and you start the truck and put it in gear, like any open differential, all the torque should be able to escape thru that raised wheel. Same thing happens if you drive the truck over a steep hump, you will loose thrust when an axle lifts off.
If the lifted wheel doesn’t start spinning and the other grounded wheels try to pull the truck off the jack, the power divider is locked…