What is the relationship between thermal energy and friction

When temperature increases, particles in an object speed up, which means an increase in thermal energy. Since the particles are moving more now, the potential energy decreases, therefore kinetic energy increases. Overall, when temp goes up, thermal energy goes up, which leads to an increase in kinetic energy. 

When an object is moving relitive to the object it uses the moving objects kinetic energy to create heat energy by shaking the substance and slowing the moving One down if you are looking for formula I suggest driving one think about how much work the friction is doing