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I recently rode my bike on some steep hills. After descending on a 4 km road with some sections at 21% slope, I realized my rims were pretty hot not only where the brake pads operate, but even up to the sprokes connection.
Though I realize that keeping the bike moving will allow for a more effective cooling, should one let the rims cool down to preserve braking efficiency in such situations?
Your braking technique is probably bad with respect to overheating. Continuing to ride could help, but only if you do periodic breaking, i.e. you don't break at all until you reach max safe speed, then you brake hard to slow maybe by 10km/h, repeat. How much speed to lose depends on slope (how fast you gain speed again) and load (how much energy is dumped into your brakes to slow the same amount). If you brake more in one go, then your brakes have more time to cool in between but your average speed is also slower. In the absolute worst case (heavily overloaded/bad brakes/too steep) you stop almost all the way and your max safe speed is also pretty low. Make sure the periods of braking are much shorter than the periods of free-rolling.
If your rim brakes become too hot you risk melting the tube (or otherwise damaging the rim, but I suspect first to go would be the tube) and at least disc brakes also just stop braking at all once they are properly overheated (I can tell you from experience, this is no fun).
If the above technique doesn't suffice, then it's too steep and/or there is too much load on your bike for this gradient and you must periodically stop and let the brakes cool or just walk your bike down the hill.
