The thermal evolution of bimetallic Cu-Ni 343- and 1000-atom nanoclusters of compositions (Cu0.25Ni0.75) and (Cu0.5Ni0.5) is examined with molecular dynamics simulations using the Sutton-Chen many-body potential function. A heating curve is constructed starting from 0 K up to 1400 K, and the melting characteristics are determined on the basis of the variations of the potential energy and heat capacity with temperature. The shape evolution of the nanoclusters is analyzed in terms of deformation parameters. It is found that the bimetallic clusters melt in two stages. The first transition, corresponding to surface melting of the external Cu layers whereas the Ni core remains solid, is located at 400-500 K depending on the overall composition and cluster size. The second transition corresponds to homogeneous melting and takes place in the range of 700 to 900 K depending on the nanocluster size and composition. Thus, the melting temperature is much lower than those of bulk Cu and Ni, and the heat capacity shows a broader peak. At temperatures just before the melting transition, the heat capacity curves exhibit either a shoulder or an extra peak attached to the main melting transition peak; this is associated with isomerization structural transitions due to the diffusion of Cu atoms toward the cluster interior.