The intensity of H3+ emission can be driven by both temperature and density, and when fitting a set of infrared H3+ line spectra, an anticorrelation between the fitted temperatures and densities is commonly observed. The ambiguity present in the existing published literature on how to treat this effect puts into question the physical significance of the derived parameters. Here, we examine the nature of this anticorrelation and quantify the inherent uncertainty in the fitted temperature and density that this produces. We find that the uncertainty produced by the H3+ temperature and density anticorrelation is to a very good approximation equal to the uncertainties that are derived from the fitting procedure invoking Cramer's rule. This means that any previously observed correlated variability in the observed H3+ temperature and density outside these errors, in the absence of other error sources, are statistically separated and can be considered physical. These results are compared to recent ground-based infrared Keck Near InfRared echelle SPECtrograph (NIRSPEC) observations of H3+ emission from Saturn's aurora, which show no clear evidence for large-scale radiative cooling, but do show stark hemispheric differences in temperature.