Individual luminescent nanoparticles enable thermometry with sub-diffraction limited spatial resolution, but potential self-heating effects from high single-particle excitation intensities remain largely uninvestigated because thermal models predict negligible self-heating. Here, we report that the common "ratiometric" thermometry signal of individual NaYF4:Yb3+,Er3+ nanoparticles unexpectedly increases with excitation intensity, implying a temperature rise over 50 K if interpreted as thermal. Luminescence lifetime thermometry, which we demonstrate for the first time using individual NaYF4:Yb3+,Er3+ nanoparticles, indicates a similar temperature rise. To resolve this apparent contradiction between model and experiment, we systematically vary the nanoparticle's thermal environment: the substrate thermal conductivity, nanoparticle-substrate contact resistance, and nanoparticle size. The apparent self-heating remains unchanged, demonstrating that this effect is an artifact, not a real temperature rise. Using rate equation modeling, we show that this artifact results from increased radiative and non-radiative relaxation from higher-lying Er3+ energy levels. This study has important implications for single-particle thermometry.