Its the other way around . Atomic motion, a vibration of an atom in this instance, generates heat . That heat in contact with another surface will vibrate the atoms in the other substance . That is conduction .
Gases react with heat by being pushed upward (away from gravity's pull) by cold pushing underneath and thus hot gases rise . The denser cold atoms have more attraction to the earth . That is convection .
Radiation is where the electron levels emit a certain band of radiation due to the agitation and vibration of the atom they are orbiting .
Heat is a measurable quality . Heat transference is measurable only by the heat of what it left compared to the heat of where and what it affected .
Absolute zero is where no atomic vibration (heat) exists .
Heat itself, as I remember what little physics I studied, was the result of motion
The motion you may mean is the atomic vibration that results from excess energy within a substance causing it to loosen its bonding with other similar atoms or those within a structure, perhaps crystalline in nature . This loosening takes a substance through the four stages of matter, solid, liquid, gas, plasma . Because of its uniqueness, it may be worth putting in absolute zero as a 5th state, but I dont think it has been achieved yet (very close though) .