A few mm of thickness will make no practical difference to the temperature of the brake fluid.
Did I mention the temperature of the brake fluid?
You mentioned brake fade which nowadays only occurs on the race track, or perhaps descending an Alp with a heavy caravan. Boiling brake fluid causes it. Very hot surface brake pad material can also cause it irrespective of how thick the pad is. Indeed, with severe use it is more likely to occur with new pads yet to bed in.
Forget the physics, a pad with 1mm needs changing NOW
Agreed, apart from forgetting physics, an understanding of which is essential for fully understanding the workings of a car.
However, a 10mm thick pad has at least 8mm of use. With normal driving, front pads should last at least 40,000 miles - probably double that on the rear (e.g.my heavy Audi, still has 3-4mm after 71,000 miles). If the OP has 3mm, at 5000 miles per millimetre, he should be able to do well over 6000 more miles before they fail the MoT 1.6mm limit.
I repeat - waste not want not.
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