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do the rotors on the 300c get really hot even if just braking from cruising speeds?
Hot enough that I wouldn't touch them with your fingers! But not as hot as the smaller brakes on the 2.7 liter and 3.5 liter (RWD) 300 models.

When you're cruising, the kinetic energy of your vehicle is equal to 1/2 the mass of the car times the square of the velocity. (E = 1/2 M * V^2)

When you brake to a stop, most of that kinetic energy is converted into thermal energy and briefly stored in your rotors. Let's calculate how much energy (in joules) is in a 4,000 pound Chrysler traveling at 75mph:

Convert 75mph to meters per second = 33.53 meters/second

Convert 4,000 pounds to kilograms = 1814.4 Kg

Energy = 1/2 * (1814.4) * (33.53 * 33.53) = 1,019,929 joules. A joule is the work done to produce one watt of power continuously for one second. So that's nearly enough energy to light up two 150 watt light bulbs for an hour. It is not surprising that the brake rotors are hot.

Disclaimer: I've made some simplifying assumptions, ignoring the contribution of wind resistance in slowing the car and ignoring the drag of the drive train. Some of the energy at cruising speed is converted to heating the air by the body of the car. And some goes into heating the drivetrain. But most of the kinetic energy is converted into thermal energy by the brakes. And to the point of the previous post by Cibalo, I've assumed the stop took place over a short enough distance that the rotors didn't have time to cool off significantly.
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