Why is the heat flow in metals slower than the current flow?
The current flows almost instantaneously because it is driven by an electric field which appears across the conductor almost instantaneously (near the speed of light). All electrons in the conductor are set into motion by a chain reaction. Collectively they all move through the conductor at what is called the drift velocity at the same time.
By contrast, heat transfer by conduction requires the transfer of energy by collisions between particles in the material that starts at the high temperature end of the conductor and progresses gradually to the low temperature end of the conductor. In the case of metals, the particles are primarily electrons.
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