This APU had a history of auto-shutdowns for high oil temperature. We ran the APU over two hours and confirmed the APU oil is heating up, causing the high oil temp auto shutdown. The oil cooler could have been clogged or the thermal bypass valve that regulates the oil flow through the oil cooler by its temperature. With a thermal imager, we noticed the oil cooler exhaust air temperature reduce over time from 165 degrees F down to 120 degrees F as the oil heated up from 225 degrees F to 310 degrees F at the scavenge oil fitting just above the chip detector, which is the oil temp auto shutdown trigger point for the ECU. The thermal bypass valve was the same temperature as the scavenge oil at the inlet and outlet ports and the scavenge T fitting at the bottom of the engine.
The oil is not cooling as it should.
We ended up replacing the oil cooler and bypass valve as an assembly. The readings afterward were as follows: oil cooler exhaust temperature was 180 degrees F, scavenge oil fitting temperature was 215 degrees F. At this point, I did finally take a reading from the oil pressure filter housing. The temperature about matched the oil cooler exhaust... 180 degrees F. Problem solved.
The interesting point is what the thermal imager could do for troubleshooting this issue. The oil cooler exhaust should run about the same temperature as the oil in the outlet line from the oil cooler and the oil pressure filter housing.
If the exhaust port outside is significantly cooler than the filter housing or the outlet, look to the thermal bypass valve.