Agree that 105 is not hot. Our 2000 XJ always runs on 100. The only time our temp ever went over 100 on the west coast is when we did a long climb and then pulled up for a squiz at a view. Numbkins here had a brain fade and switched the engine off straight away instead of leaving it running. When I started it back up 5 minutes later the temp was up to 107. Went back down to 100 within 3 minutes.
If your temp is stable without a trailer it should do the same with a trailer.
I never worry about locking out overdrive, highway towing in 4th is fine, the auto looks after everything.
Have fun, they are a great tow vehicle.