  We have studied thermal gradients in thin Cu and AlMn wires, both
experimentally and theoretically. In the experiments, the wires were Joule
heated non-uniformly at sub-Kelvin temperatures, and the resulting temperature
gradients were measured using normal metal-insulator-superconducting tunnel
junctions. The data clearly shows that even in reasonably well conducting thin
wires with a short ($\sim 10 \mu$m) non-heated portion, significant temperature
differences can form. In most cases, the measurements agree well with a model
which includes electron-phonon interaction and electronic thermal conductivity
by the Wiedemann-Franz law.
