  Flux limited X-ray surveys of galaxy clusters show that clusters come in two
roughly equally proportioned varieties: "cool core" clusters (CCs) and
non-"cool core" clusters (NCCs). In previous work, we have demonstrated using
cosmological $N$-body + Eulerian hydrodynamic simulations that NCCs are often
consistent with early major mergers events that destroy embryonic CCs. In this
paper we extend those results and conduct a series of simulationsusing
different methods of gas cooling, and of energy and metal feedback from
supernovae, where we attempt to produce a population of clusters with realistic
central cooling times, entropies, and temperatures. We find that the use of
metallicity-dependent gas cooling is essential to prevent early overcooling,and
that adjusting the amount of energy and metal feedback can have a significant
impact on observable X-ray quantities of the gas. We are able to produce
clusters with more realistic central observable quantities than have previously
been attained. However, there are still significant discrepancies between the
simulated clusters and observations, which indicates that a different approach
to simulating galaxies in clusters is needed. We conclude by looking towards a
promising subgrid method of modeling galaxy feedback in clusters which may help
to ameliorate the discrepancies between simulations and observations.
