I'll inject my two cents on the whole "diff cooler" argument.
Short answer: None of the S197 owners reading this probably
need a diff cooler. If you trust me, you can stop reading there. Yes, the Track Pack cars and Laguna came with diff coolers, but it was mostly for marketing. Those cars also had Torsen differentials and fairly low power/grip levels and likely didn't ever get the diff fluid hot enough to matter.
Long Answer: Depending on the model S197 you have, the limited slip differentials (LSD) type you run, power level being tracked at, and how you use the car/LSD on track (pro level / endurance level abuse) - you
might need a diff cooler. Professional road race drivers tend to run much longer sessions, drive their cars hard, "use" the differentials much more aggressively than HPDE folks that drove their car to a track event. for pro teams a diff cooler makes sense and probably extends the service life of their consumables: Diff fluid and LSDs. But are Pro level racers in Mustangs looking at this form and asking these questions? No.
Let's look at some of the history of Mustang LSDs and coolers. For the longest time Mustangs came with clutch style LSDs in a large, steel, "solid axle" housing with no factory differential fluid coolers. LSDs and 8.8" solid axles have been in Mustangs for a long time - since the V8 1986 model from the Fox era, through SN95 (exception: 99-04 Cobra), and all through the S197. So we have had 30 years of the same basic 8.8" solid axle and Traction Lock LSD (exception: Boss302 and Track pack S197s had a Torsen LSD).
I was tracking a 5.0L Fox Mustang with an 8.8" solid axle and clutch LSD since 1990, and didn't see any reason for a diff cooler then. Why? Power levels were much lower back in those days for a vast majority of people running these cars on a road course (HPDE events were a very new concept in those days and Time Trials almost unheard of). Starting with the 99 Cobra some select few folks did see some heat issues with IRS equipped SN95 cars, and the 2000 Cobra R model came with a "trunk kit" that included a diff cooler.
What was different on the 2000 Cobra R were: higher power and a much smaller differential housing (IRS).
The 2000 R model's unique 5.4L DOHC V8 made some real power from the factory, for once. And unlike the supercharged 03-04 Cobras, it wasn't supercharged so it could be driven for more than 2 laps before the engine overheated... the 00 R was a competition model and was raced professionally.
Most Mustang folks today don't have heat problems in S197s until they get into the higher powered cars, or giant race tires, or serious abuse on a road course. And even then... most folks who think they have heat problems don't have any real hard data or failures to point to, just "internet wisdom".
Now personally we DID run into some problems with differential heat on our TT3 Mustang. Burned up two sets of outer axle seals, the diff fluid kept getting cooked, etc. But we traced a LOT of this problem to the clutch style Ford Traction Lock differential.
We were burning clutch packs up in 2 track days after the car got more serious in 2013, and my guys at the shop got tired of replacing the carbon clutch packs. The LSD was getting cooked because
HOW IT WORKS creates heat.
After we moved to a Torsen T2-R differential, all of those heat problems went away. The fluid wasn't getting burned, the seals weren't melting, and the same differential was used from late 2013 through today. Worked great, no wear items to worry about, and the fluid did run cooler.
If we would have (foolishly) stayed with the clutch-style LSD then yes, we would have technically been a good candidate for a diff cooler. But going to the Torsen dropped over a second a lap from our times (track to track testing) and the diff temps were never an issue again.
Down Sides to a Diff Cooler
There are downsides to adding a diff cooler to your Mustang, namely:
1. Cost + added weight + added complexity of use (you have to remember to turn the cooler on/off)
2. More places for fluid to leak (hoses, heat exchanger fittings)
3. These pumps are pushing THICK fluid and takes some electrical power to run
Mostly adding a diff cooler adds new places for leaks to form, which is the main downside. That and the cost. Expect to pay $1000+ in parts and labor for a quality, functional differential fluid cooler, other than a junkyard sourced OEM unit.
Cheers,