You would likely be surprised at the Transmission and Diff temps ...
I have a tranny and diff cooler in my RX-8 track car....tranny temps will easily hit 250+ after about 15 minutes at 90 deg track temps. Diff with a Kazz clutch LSD have been over 300 without the cooler ( way over actually
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With the coolers installed they sit below 225 at all times.
I forgot to turn the pumps on and got the oil too hot.......turned on the pumps...and proceeded to melt the pump housing on the diff pump. Learned the hard way to turn everything on before GO