  Crucial to analyze phenomena as varied as plasmonic hot spots and the spread
of cancer in living tissue, nanoscale thermometry is challenging: probes are
usually larger than the sample under study, and contact techniques may alter
the sample temperature itself. Many photostable nanomaterials whose
luminescence is temperature-dependent, such as lanthanide-doped phosphors, have
been shown to be good non-contact thermometric sensors when optically excited.
Using such nanomaterials, in this work we accomplished the key milestone of
enabling far-field thermometry with a spatial resolution that is not
diffraction-limited at readout.
  We explore thermal effects on the cathodoluminescence of lanthanide-doped
NaYF$_4$ nanoparticles. Whereas cathodoluminescence from such lanthanide-doped
nanomaterials has been previously observed, here we use quantitative features
of such emission for the first time towards an application beyond localization.
We demonstrate a thermometry scheme that is based on cathodoluminescence
lifetime changes as a function of temperature that achieves $\sim$ 30 mK
sensitivity in sub-$\mu$m nanoparticle patches. The scheme is robust against
spurious effects related to electron beam radiation damage and optical
alignment fluctuations.
  We foresee the potential of single nanoparticles, of sheets of nanoparticles,
and also of thin films of lanthanide-doped NaYF$_4$ to yield temperature
information via cathodoluminescence changes when in the vicinity of a sample of
interest; the phosphor may even protect the sample from direct contact to
damaging electron beam radiation. Cathodoluminescence-based thermometry is thus
a valuable novel tool towards temperature monitoring at the nanoscale, with
broad applications including heat dissipation in miniaturized electronics and
biological diagnostics.
