Not a 737 pilot, but I do play one on the computer.
The autobrakes on the 738 might be a bit overzealous, or the pilots wanted to hit a specific exit on the runway after landing, and set them high (this would not surprise me depending on the runway they landed + what gate they are taxiing to). Or they didn't want to go hard on the reversers on landing, so they relied more on brakes than engine. Or they were a bit heavy on manual braking.
First blush I'd guess it sounds like they cooked their brakes a bit from procedure more than design, but our resident former 73 pilot probably does know.
That said ... they also have brake fans on those things, to be used when the brakes get hot. Seems weird they'd need more cooling between landing and full turnaround, but maybe on a really fast turnaround? Dunno.