RE: ABS
I've seen the mpegs some of these people posted and the photos. They weren't doing 1 second power brakes nor had they done it only once in their lifetime. I think your formula is a little off but close enough
The tranny will live a bit longer than the 213 miles but that's just my opinion. I don't believe the flash point will be reached for all the oil in the tranny simply because oil is an insulator but enough will be damaged to destroy the lubricity and dramatically shorten the transmissions life. As to the ABS portion, I thought that was covered in my original post. If the front tires are stationary and the rear tires are moving the ABS system sees a problem. If you override the system it complains.
I should also add that I am biased because I have to fix these peoples cars. I hear the "I only did it the one time" excuse a lot then open up what was a new tranny and see incredible damage. I've seen tranny oil go from healthy pinkish red to carmel colored in a week by drivers that "only did it once". Fixing intentional abuse _has_ tainted my outlook so I may sound harsh, in reality I treat this as simply a discussion of no moment. I think Jerry posted some info on trans temp and its corrolation with trans life on another web site. I wish he'd post more often as I find his insight interesting. He makes me think and I like that.
I had done some backyard testing a few years back with a car that was used as a test mule. Plain old Chevy 350 engine, TH350 trans and 24K gvw B&M tranny cooler in conjunction with the in radiator tranny cooler in the big block radiator. Tranny had a mild B&M shift kit and the engine was a mild 4v model. Using a B&M trans temp gauge on the remote trans oil filter the normal operating temperature of the transmission was 180 degrees in 80 degree weather. Water temperature was a consistent 180 degrees regardless of outside air temperature. Converter was a stock 1800 rpm 12" model. Fan was a very large heavy duty clutch type. This car got seriously abused to test loads of parts etc before the parts etc would be allowed on the real cars. It was a lot of fun and had a boat load of tricks
I kind of miss that car.
Power braking the car for 5 seconds raised the transmission oil temperature to 220 degrees. The tranny needed to be driven for about 5 minutes at highway speeds to cool back down to normal. Power braking for 10 seconds raised the tranny temp to 250 degrees and took about 10 minutes to bring it back down to normal. Not too bad but not something you want to do too ofter either.
For the last one I did it drag style. Power braking for 5 seconds, rolling forward about 10' with the tires still spinning to simulate the tire warm up then bringing the car back to a full stop, doing another short power brake to launch the car then releasing the brake but maintaining the burn out for as far as it would go then continuing down the quarter mile under full throttle for a full speed run for the duration of the 1/4, lifting at the finish line and bringing the car back down to return lane speed. Trans temperature hit 280 degrees and took about twenty minutes of high speed driving to bring it back down to normal.
In those few runs the engine water temperature never went over 190 degrees. Since the trans temperature was taken out near the radiator the temperature seen on the gauge is undoubtedly lower than the internal transmission oil temperature. However, for less than 20 seconds of hard use it still hit a very high temperature and took a long time to come back down again. MK VIIIs don't have nearly the cooling capacity of that test car so the Lincoln temps may be worse and it will definitely take a MK VIII much longer to cool back down again. I also took the trouble to cool the tranny back down again whereas many people do not. If that oil pump isn't spinning that oil isn't being cooled, it's being cooked.
I don't expect anyone to believe this stuff. Try it yourself, it isn't expensive or hard to do. You just need a trans oil temp gauge and a few moments of track time. Don't take my word for it, you don't know me from Adam.