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 (∼10μm) 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.
@article{arxiv.cond-mat/0607809,
title = {Influence of temperature gradients on tunnel junction thermometry below 1 K: cooling and electron-phonon coupling},
author = {J. T. Karvonen and L. J. Taskinen and I. J. Maasilta},
journal= {arXiv preprint arXiv:cond-mat/0607809},
year = {2007}
}