  We present a method for nanoscale thermal imaging of insulating thin films
using atomic force microscopy (AFM), and we demonstrate its utility on VO$_2$.
We sweep the applied voltage $V$ to a conducting AFM tip in contact mode and
measure the local current $I$ through the film. By fitting the $IV$ curves to a
Poole-Frenkel conduction model at low $V$, we calculate the local temperature
with spatial resolution better than 50 nm using only fundamental constants and
known film properties. Our thermometry technique enables local temperature
measurement of \textit{any} insulating film dominated by the Poole-Frenkel
conduction mechanism, and can be extended to insulators that display other
conduction mechanisms.
