Heat transfer between a silver nanoparticle and surrounding water has been studied using molecular dynamics (MD) simulations. The thermal conductance (Kapitza conductance) at the interface between a nanoparticle and surrounding water has been calculated using four different approaches: transient with/without temperature gradient (internal thermal resistance) in the nanoparticle, steady-state non-equilibrium and finally equilibrium simulations. The results of steady-state non-equilibrium and equilibrium are in agreement but differ from the transient approach results. MD simulations results also reveal that in the quenching process of a hot silver nanoparticle, heat dissipates into the solvent over a length-scale of ~ 2nm and over a timescale of less than 5ps. By introducing a continuum solid-like model and considering a heat conduction mechanism in water, it is observed that the results of the temperature distribution for water shells around the nanoparticle agree well with MD results. It is also found that the local water thermal conductivity around the nanoparticle is greater by about 50 percent than that of bulk water. These results have important implications for understanding heat transfer mechanisms in nanofluids systems and also for cancer photothermal therapy, wherein an accurate local description of heat transfer in an aqueous environment is crucial.