The energy transferred between samples of matter because of a difference in their temperatures is called

Heat is energy in transit, that is, transfer of (thermal) energy from one body or system to another.

In other words, when you have two bodies with different temperatures and thermal energy is transferred from one body to another, implying a high speed and kinetic energy in the particles involved, we are talking about heat.

When both bodies or the complete system reaches the thermal equilibrium (they are at the same temperature) the process is over and there is no heat.

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