  Considering a copper wire heated by Joule effect and the variation of its
resistivity and specific heat with temperature, we established numerical and
analytical solutions (between 293 and 1356 K for the latter) for the evolution
of its temperature over time. The Temperature vs. Time evolution follows a
Lambertian function. The calculations are based on the assumption of adiabatic
heating and uniform current distribution within the wire. We demonstrate that
at very low temperature the heating rate is strongly dependent on copper
purity.
