I don't know about a quantum mechanical description, but a classical description would say that the average kinetic energy of the modes of oscillation among the constitutive molecules in bodies t1 and t2 would try to seek equilibrium. This would be manifested as the transfer of heat. How does that happen? Probably in a fashion similar to the volume conduction of current in biological tissue, or..How about this? You're at a party and you and all your friends are jacked up on adrenaline becasue you're having so much fun. However, its your house and you know the noise complaints are coming soon. So..you grab one of your friends who's bouncing off the walls and try to calm him down..So far so good until another buddy comes flying across the room and now you have to grab him too and calm him down. Of course it doesn't take doing this to too many other buddies before you begin to get tired and "cool" down. Of course, by this point, everyone has cooled down a bit, and now the party is more manageable
To put it another way, it's a propagation effect, like falling dominoes, a mechanical agitation that spreads radially from the heated source until equilibrium is achieved in the bounded system.
Did that help?