The characterization of heat capacity anomalies in a two-dimensional nanocluster is presented. Calculations of the heat capacity as a function of temperature show the presence of two coexistence regions. The first region corresponds to a solid/liquid coexistence and the second to a liquid/vapor equilibrium. These two transitions observed are analogous to melting and evaporation transitions observed in various two-dimensional bulk systems. The standard Metropolis Monte Carlo algorithm fails in the identification of these transitions due to quasiergodicity problems. The implementation of the classical J-walking algorithm reduces this problem, and allows the precise identification of these two transitions.