That, of course, segues into the real reason an electron cannot be at rest: the Heisenberg Uncertainty Principle. If an electron were at rest, it would be at a well-defined location with a well-defined momentum.
Being senile and working from memory at the same time, I was recalling the "you can't get to absolute zero" statement of the 3rd law. Now that I've looked it up, this is Nernst's Heat Theorem statement of the 3rd law from 1907. I'm getting as bad as medved.
So for the unbound electron, I was reasoning that since it couldn't get to zero temperature, the classical picture of it would mean it still had velocity. I see what you were saying Phys, since the temperature of a gas is the result of the average velocity of all the particles, this is not exactly the best approach for a single particle. But quantum mechanics makes my head hurt. The uncertainty approach was much more elegant.
While I'm at it, I'm looking at Kelly's "Thermodynamics and Statistical Physics" and in the chapter on the 3rd law under the section "Exceptions and Restatement" (no snickering from the Creationists please), there is this little gem,
"Thermodynamics...can make no positive statements about transformations which begin or end in nonequilibrium states."
I forgot all this adiabatic stuff, but it sure makes it difficult to apply the 2nd law to living organisms. I'm going to have to get some newer books.