  We report transport measurements as a function of bias in open semiconductor
quantum dots. These measurements are well described by an effective electron
temperature derived from Joule heating at the point contacts and cooling by
Wiedemann-Franz out-diffusion of thermal electrons. Using this model, we
propose and analyze a quantum dot based sensor which measures absolute magnetic
field at micron scales with a noise floor of $\sim 50 \mu\phi_{0} / \sqrt{Hz}$
at 300 mK.
