Does coefficient of friction depend on temperature? So I was thinking of brakes in a car the other day. When brakes are applied, the forward force is converted to heat in the brake disks. When brakes are cool (at the beginning) they have the ability to absorb a lot of heat and have more braking power. But as the brakes heat up, their ability to absorb more heat should decrease and in turn the braking force also decreases.
So, does this mean that the coefficient of friction decreases with temperature? If so, how does this work microscopically? Normally the coefficient of friction is a measure of how smooth or rough the two surfaces are, how would heat factor in?
 A: Well,in short,yes.
Though this variation is largely material dependent, with change in temperature, the internal mechanism causing friction (old or modern mechanism) varies.So value of coefficient of friction changes.
Generally,this value decreases with increase in temperature.
Going with the modern mechanism,with increase in temperature, the intermolecular forces between surfaces decrease. This is similar to the fact that with increase in temperature a solid melts and a liquid vaporises.Hence friction decreases.

P.S. I am assuming that you know the mechanism of friction because the way you described phenomenon is remarkable. In case,you need more detailed explanation comment below.
A: As stated in the answer provided earlier, in general it is the case that a higher temperature of the brakes comes with lower coefficient of friction.
This loss of coefficient of friction is known as 'brake fading'.
Brake fading is very dangerous of course. Say a car has completed a lap, on a circuit that is hard on the brakes, and the driver is approachng the same corner again, with the same velocity as in the first lap. Now the brakes no longer have the same braking power.
However, it is not the case that every material will display brake fading. Materials have been developed that retain a high coefficient of friction when they are red hot. These materials are used in racing.
I remember seeing a demonstration of that in a television program.
A powerful car was outfitted with brake pads and brake disks made of such a very expensive material. A racing driver took the car for a number of laps, all the time braking as agressively as safely possible. With the brakes very hot the car came back to the camera, and the camera swooped in on one of the wheels to show the brake disk glowing red hot. The driver confirmed the brakes had not displayed any noticable brake fading.
