Suppose there are two similar particle-like objects attempting to "bump" against each other to create friction, they are prevented from colliding against one another due to either electrostatic repulsion or Pauli exclusion principle. My question is how friction (heat) is produced in the above stated scenario. Am I mistaken as in classical physics, when two rough surfaces slide against each other, heat is generated and what does quantum physics say about it?
You've stumbled on an interesting idea: how do classical systems that dissipate heat or energy via friction arise from quantum systems that perfectly conserve energy in their interactions? Particles in the collision kind of scenario you described don't really exhibit friction.
One convenient point is that temperature and heat transfer in quantum physics is very similar to the classical physics case. To give something of an idea within the regime of classical physics, let's imagine our surfaces as having small bumps and crevices, but still large enough as to be governed by classical mechanics. As the two surfaces slide along each other, the bumps on either surface collide against each other. These collisions cause shock waves, which will disperse and travel through the material in a chaotic fashion, resulting in what's effectively a random vibrational movement. Temperature is to an extent a measure of this random movement.
Looking back to your scenario of two quantum particles colliding, you could consider this as the collision step in the above explanation, except at the quantum level. An important point to note is that temperature is related to both the energy of the particles, as well as how chaotic or randomly they're behaving. In this way, two particles undergoing a simple collision can't really be described in terms of temperature. The motion has to have a degree of randomness or chaoticness for there to be temperature. Quantum particles are usually described in terms of probabilities anyways, so they're well-suited to temperature descriptions.
Whatever you do it produces heat. This has to do with electromagnetic interactions between the two objects which interact. Moving one surface on an other, the surface electrons from both surfaces will be disturbed, they couldn't be at the same place and will be moved slightly. Every displacement has elements of acceleration and any acceleration is escorted by electromagnetic radiation. This EM radiation is called radiation because it flies away from the source. This energy transfer is what we see as heat radiation. The loss of energy for every mechanical process is based on this phenomenons.