What condition must be met for conduction to occur between two objects?

For conduction to occur, it is necessary for two objects to be in contact and for there to be a temperature difference between them. This temperature gradient is what drives the transfer of thermal energy from the hotter object to the cooler one. Heat moves from areas of higher energy (higher temperature) to areas of lower energy (lower temperature) until thermal equilibrium is reached.

If the objects are at the same temperature, there will be no net energy transfer, and therefore conduction will not take place. Additionally, for conduction to happen, the objects generally need to be good conductors of heat; while insulators can slow down heat transfer, they cannot facilitate conduction. Thus, the requirement of contact combined with a difference in temperature is essential for conduction to occur effectively.