cooker and 79pmooney have it all about right. As for the conundrum about heat, that's not wrong either. Yes the brake pads dissipate heat and this is an important function because the collision between the bike and the ground is an inelastic one where both mechanical energy and momentum cannot be conserved at the same time. While all momentum goes to the ground, all kinetic energy is dissipated. In an elastic collision you would bounce off a wall attached to the earth and would end up going the opposite direction.

You could instead slow the bike by running into a big rubber band. Right as you stop you could imagine clipping the rubber band so it doesn't spring back. In that case no heat was dissipated. That energy was stored in the rubber band and could be dissipated in some other braking mechanism later. Would you call that mechanism the stopping force? It does the same job as the brake pads. You might argue the band and the transfer of energy to it replaced the brake pads. That's another way to see it, but the band applied the same external force as the ground does during normal braking. In the end the point is the external force from the band is still the same as the force would have been from the ground for the same deceleration curve. That force requirement remains the same regardless where the energy goes.

These are somewhat separable issues and is related to why I said it's hard to exactly assign blame to forces. My force balance was however correct and the rearward force that decelerates the frame and rider requires large involvement of the spokes.