The temperature coefficient of good conductors like metal is positive. So with increase in temperature resistance increases and conductance decreases. With decrease in temperature resistance decreases and conductance increases. So will metal conduct at absolute zero? But every motion ceases at absolute zero. And electric conduction is due to motion of electron
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In real world, most of the conductors become superconductors even before $0K$. Where their resistivity goes to zero. – Ari Apr 02 '20 at 10:22
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1This seems to be essentially an electronic variant of this question (and many others like it on this site) The short answer is that at absolute zero there is not random motion of particles, but if you push them (say with an electric field) they will still move. – By Symmetry Apr 02 '20 at 10:31