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Regarding the mesh on the shoe, one solid quadratic element through the thickness is generally insufficient to capture the stress due to bending of the material. A minimum of two solid quadriatic elements should be used.
Brakes get hot from the friction, normal force, and surface velocity integrated over time between the brakepad and the brakedrum. Is your model generating heat by this method? Heat would be conducted away from the surface the pad slides on to the rest of the drum and convection cooling could transfer the heat to the ambient air.
I advise you to make a very simple two body model of a disc plate with a center hole. Mesh the disc with 4 elements through the thickness and a small pad of equal thickness on the top of the disc positioned so it is near the outer diameter of the disc.
Make it a symmetric model so that you only have a half-thickness disc. The symmetry boundary conditions will keep the disc from bending, it will be as if there is a pad on the other side pushing up. Put a revolute joint on the face of the hole in the disc and use a rotational load to rotate the disc. Mesh the pad with 4 elements through the thickness. Put a translational joint to ground on the top of the pad. Add a Joint Load of Force to press the pad into the disc. Frictional contact between the pad and disc will create the heat source along with the rotation and the normal force. In a Transient Structural model, you should be able to see the disc and pad warm up over time. You don’t need any other heat transfer boundary conditions. First step is to show a temperature result that is higher than the 20C initial temperature.
Good luck!