  Solid-state emitters such as epitaxial quantum dots have emerged as a leading
platform for efficient, on-demand sources of indistinguishable photons, a key
resource for many optical quantum technologies. To maximise performance, these
sources normally operate at liquid helium temperatures ($\sim 4~\mathrm{K}$),
introducing significant size, weight and power requirements that can be
impractical for proposed applications. Here we experimentally resolve the two
distinct temperature-dependent phonon interactions that degrade
indistinguishability, allowing us to demonstrate that coupling to a photonic
nanocavity can greatly improve photon coherence at elevated temperatures up to
$30~\mathrm{K}$ that are compatible with compact cryocoolers. We derive a
polaron model that fully captures the temperature-dependent influence of
phonons observed in our experiments, providing predictive power to further
increase the indistinguishability and operating temperature of future devices
through optimised cavity parameters.
