I am unwilling to believe that there is appreciable heat flow
*along* the wire. If the ice cube is melting then icewater is
running down the wire anyway.
A calculation of this phenomenon reveals that the thermal
conductivity of the wire is important, but only because heat
is conducted *across* the wire from top to bottom. This is a
standard problem in thermo courses (e.g. Zemansky & Dittman,
Sixth Ed., p. 269). Zemansky published the solution in The
Physics Teacher for October 1965, p. 301. The title of the
paper is "Regelation of Ice is a Complicated Phenomenon",
but then he goes on to solve the problem in a straightforward
manner. Most of my (second year) students succeed in solving
the problem.
Igal, I can think of one or two sources I might consider to
be more authoritative than the one you cite. A nylon thread
should also go through the cube, but much more slowly. Does
Hewitt claim that heat is conducted in from the room or
across the wire?