  We analyze HCN and HNC emission in the nearby starburst galaxy NGC 253 to
investigate its effectiveness in tracing heating processes associated with star
formation. This study uses multiple HCN and HNC rotational transitions observed
using ALMA via the ALCHEMI Large Program. To understand the conditions and
associated heating mechanisms within NGC 253's dense gas, we employ Bayesian
nested sampling techniques applied to chemical and radiative transfer models
which are constrained using our HCN and HNC measurements. We find that the
volume density $n_{\text{H}_{2}}$ and cosmic ray ionization rate (CRIR) $\zeta$
are enhanced by about an order of magnitude in the galaxy's central regions as
compared to those further from the nucleus. In NGC 253's central GMCs, where
observed HCN/HNC abundance ratios are lowest, $n \sim 10^{5.5}$ cm$^{-3}$ and
$\zeta \sim 10^{-12}$ s$^{-1}$ (greater than $10^4$ times the average Galactic
rate). We find a positive correlation in the association of both density and
CRIR with the number of star formation-related heating sources (supernova
remnants, HII regions, and super hot cores) located in each GMC, as well as a
correlation between CRIRs and supernova rates. Additionally, we see an
anticorrelation between the HCN/HNC ratio and CRIR, indicating that this ratio
will be lower in regions where $\zeta$ is higher. Though previous studies
suggested HCN and HNC may reveal strong mechanical heating processes in NGC
253's CMZ, we find cosmic ray heating dominates the heating budget, and
mechanical heating does not play a significant role in the HCN and HNC
chemistry.
