The factor that prevents conduction from occurring is the presence of different temperatures. When objects are at different temperatures, heat energy will flow from the object at a higher temperature to the object at a lower temperature. This transfer of heat occurs through conduction, where molecules transfer energy by colliding with neighboring molecules.
In the context of the question, if the objects have equal temperatures, there would be no temperature difference to drive the flow of heat through conduction. Therefore, equal temperatures prevent conduction from taking place.
On the other hand, when objects have different temperatures, heat will naturally flow from the warmer object to the cooler one until thermal equilibrium is reached. This difference in temperature creates a gradient that drives the conduction of heat between the objects.
