  On-chip demagnetization refrigeration has recently emerged as a powerful tool
for reaching microkelvin electron temperatures in nanoscale structures. The
relative importance of cooling on-chip and off-chip components and the thermal
subsystem dynamics are yet to be analyzed. We study a Coulomb blockade
thermometer with on-chip copper refrigerant both experimentally and
numerically, showing that dynamics in this device are captured by a
first-principles model. Our work shows how to simulate thermal dynamics in
devices down to microkelvin temperatures, and outlines a recipe for a
low-investment platform for quantum technologies and fundamental nanoscience in
this novel temperature range.
