You are cupping a small furnace in your hands, and the warmth you feel is a lie about touching.
Your palm never contacts the ceramic. The outer electrons of the mug's atoms and the outer electrons of your skin repel each other electrostatically, so what registers as solid, comforting pressure is a force field standing off a gap you will never close. You are holding the mug the way two magnets held apart hold each other.
The heat is more honest. Inside, the coffee is a riot of water molecules moving at roughly the speed of a passenger jet, colliding billions of times a second, and each collision with the inner wall nudges a ceramic atom into a slightly harder jiggle. That jiggle propagates outward, atom to atom, until it reaches your nerve endings, which report "warm" without ever mentioning that they are simply being informed of statistics.
Temperature is just the average frantic-ness of things too small to see.
And it is all running downhill. The mug is a machine for losing. Every second it radiates infrared photons into the room and bleeds jiggle into the air, and the second law guarantees the coffee will cool to room temperature and never, ever spontaneously reheat. You are watching an ordered pocket of energy disperse into disorder, which is the same one-way arrow that distinguishes the future from the past.
The mug going cold is, in miniature, the reason time only points forward.
The ceramic itself was mud, silicate minerals crushed out of ancient rock, fired until the atoms locked into a rigid disordered lattice, a frozen liquid pretending to be a solid.
Those silicon atoms were forged in the core of a dying star and flung across the galaxy before the Sun existed.
You are drinking from a cooled fragment of a supernova, and it is getting cold because everything does.