Single-walled carbon nanotubes (SWCNTs) are promising absorbers and emitters to enable novel photonic applications and devices but are also known to suffer from low optical quantum yields. Here we demonstrate SWCNT excitons coupled to plasmonic nanocavity arrays reaching deeply into the Purcell regime with Purcell factors (F P) up to F P = 180 (average F P = 57), Purcell-enhanced quantum yields of 62% (average 42%), and a photon emission rate of 15 MHz into the first lens. The cavity coupling is quasi-deterministic since the photophysical properties of every SWCNT are enhanced by at least one order of magnitude. Furthermore, the measured ultra-narrow exciton linewidth (18 μeV) reaches the radiative lifetime limit, which is promising towards generation of transform-limited single photons. To demonstrate utility beyond quantum light sources we show that nanocavity-coupled SWCNTs perform as single-molecule thermometers detecting plasmonically induced heat at cryogenic temperatures in a unique interplay of excitons, phonons, and plasmons at the nanoscale.