Just been revising for my next SIM and found this: FCOM PER-LDG-GEN 'Use of the autobrake system'
..........furthermore, it ensures a straight roll-out............
So, as I suspected, the autobrake
does keep the aircraft straight on the runway, and therefore, with a crosswind, the downwind brake will do more work to prevent weather cocking, and hence get hotter.
Thinking about it, during landing I never have to do much to keep straight in a crosswind
after the autobrake cuts in, but I do have to work the rudder/NWS to keep straight during a crosswind take-off.
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