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 characterize such emission quantitatively, and for the first time with applications 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.