The coalescence, the initial stage of sintering, of two contacted Cu nanoparticles is investigated under different heating rates of 700, 350 and 233 K/ns. The nanoparticles coalesced rapidly at the initial stage when the temperature of the system is low. Then, the nanoparticles collided softly in an equilibrium period. After the system was increased to a high temperature, the shrinkage ratio, gyration radius and atoms’ diffusion started to change dramatically. The lower heating rate can result in smaller shrinkage ratio, larger gyration radius and diffusion of atoms. However, the growth of sintering neck is hardly influenced by the heating rate. The results provide a theoretical guidance for the fundamental understanding and potential application regarding nanoparticle sintering.