Question

What are the 2 conditions for the heat to transfer by conduction

Answer 1

here is your answer

Answer 2

Two major conditions playing important role in heat transfer are the temperature difference and the tendency of the material to change it's state, in which the temperature difference is the dominating factor in most of the cases.

Whenever there is temperature difference between two bodies, the temperature difference acts as a driving force for heat to flow from high temperature body to lower one. It can be considered analogous to flow of water. Whenever you place water at a higher place, it tends to flow to a lower one.

Now there can be many conditions affecting HT rate such as presence of convecting medium (natural or induced), thermal conductivity, heat capacity, etc.