Does heat transfer cause molecules to cool down?

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gracy
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One quick question about heat transfer.
during conduction heat transfer occur when molecules collide with each other .heat from one end of the object is transferred to other end .when molecules from end 1 collide with near by molecules of end 2 they transfer their energy to those nearby molecules.My question is after transferring energy do the molecules of end 1 get colder (provided that no constant supply of heat.)
 
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Energy, even as heat, is conserved.
 
Bystander said:
If you're adding no energy to the system, and the energy of the system is conserved, the obvious conclusion is ... ?
the molecules of end 1 get colder,right?
 
Bystander said:
Yes.
And if heat is supplied continuously both ends would be hot but at any given instant end 1 which is in direct contact with heat source would be at higher temperature than end 2,right?
 
Bystander said:
So long as the source is at a higher T than end 2.
you mean source and end 1 would be at same temperature?
 
Bystander said:
Or very close.
Thanks a lot for answering all my question.Can you please have a look at my thread moment of inertia ,this would be a great help.