Heat capacity curves as functions of temperature were calculated using Monte Carlo methods for the series of Ne13-nArn clusters (0 less than or equal to n less than or equal to 13). The clusters were modeled classically using pairwise additive Lennard-Jones potentials. The J-walking (or jump-walking) method was used to overcome systematic errors due to quasiergodicity. Substantial discrepancies between the J-walking results and those obtained using standard Metropolis methods were found. Results obtained using the atom-exchange method, another Monte Carlo variant for multi-component systems, also did not compare well with the J-walker results. Quench studies were done to investigate the clusters’ potential energy surfaces. Only those Ne-Ar clusters consisting predominately of either one or the other component had lowest energy isomers having the icosahedral-like symmetry typical of homogeneous 13-atom rare gas clusters; non-icosahedral structures dominated the lowest-energy isomers for the other clusters. This resulted in heat capacity curves that were very much different than that of their homogeneous counterpart. Evidence for coexistence behavior different than that seen in homogenous clusters is also presented.