Towed my 1993 Ford Taurus for 2 years with the engine running in neutral. Never a problem and it got 100 miles to the gallon. Tested it first in the driveway, let it idle for two hours, never got hot because the electric fan comes on. Since I use a Brake Buddy, I installed a 3 way valve in the vacuum line to the power brake booster so I could vent the line so it wouldn't be power brakes when the engine idles or the brake buddy would lock them up. No problem with the power steering so far as I could tell, tires wore normally. Alot cheaper and easier than installing an axle disconnect for $1000 dollars. On the Taurus, you have to lower the sub frame to remove the front sway bar to shorten one end, weld it up and reinstall, not a simple job.
Mine had the same problem, the valve that shuts off the hot water to the unit is leaking. Controled by the knob with the blue stripe that goes to red as you turn the dial. Had the electric valve replaced and it worked for a while. then AC would not get cold, just cool because hot water is again getting into the heat exchanger. Went to Home Depot and got a ball valve, put it in the hot water line and I shut the valve when I need cold air from the AC so the hot water from the engine doesn't flow into the heat exchanger. That electric valve is not cheap.
I am the guy who towed the 1993 Taurus for 3 years with the transmission in neutral and engine idling.
Never had a problem and never overheated. You could always get a hundred dollar wireless camera to your laptop or cell phone, put it in the car and watch the temp gauge an tach. Of course the miles do rack up. The other problem is the brakes, if you have a supplemental braking system, like a Brake Buddy, you have to vent the vacuum line to the the master cyl. with a three way valve, which I got a home depot. Otherwise you will get way too much braking power and lock the wheels. I now tow my Ford Focus with manual trans. in neutral and engine off, and once I forgot to pump the brakes to get rid of the residual vacuum and the 1st time the Brake Buddy came on, I heard a loud screeching noise, the brakes locked up on the Focus. Most, if not all, auto transmission pumps work off of the input shaft, which turns when the engine is running.
As we used to say in the Aerospace Engineering Business, "One test is worth a thousand expert opinions." And alot of opinions on this forum are merely guesses from guys with a GED.
I towed a Ford Taurus, 1993, for 3 years without a driveshaft disconnect or lube pump. Simply started the engine and put it in neutral, got 100 miles to the gallon, cheaper than a lube pump. Never overheated or stopped running. When the engine is running, the auto transmission gets lubricated. Had to put a valve in the brake vacuum line to stop the power assist to the brakes so the Brake Buddy wouldn't lock up the tires when applied.
When I bought my motosat exec. system in about 2003, it worked good in CT and LA. However, when I went to FL, it couldn't lock onto the satellites. I called Motosat and they asked what may version was loaded into my unit. Turns out it was Ver. zero, they already up to Ver. 34. After I downloaded that version from their website and loaded it into the Nomad unit, it worked fine. Might want to check what version you have in your unit.