Considering the definition of conduction, conduction can occur within a single substance, but parts of the substance must have different temperatures.
What is conduction
Conduction is the mechanism of heat transfer in which thermal energy is transferred from one point to another through the interaction between the atoms or molecules of matter. In this way, heat flows from a body of a point of higher temperature to another of lower temperature.
Conduction takes place in solids, liquids and gases.
Conduction does not imply mass movement of matter. Heat, which is a form of energy, corresponds to the agitation of the atoms of matter.
Summary
Conduction can occur within a single substance, but parts of the substance must have different temperatures.
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