High Entropy Alloy nanoparticles (HEA NPs) have been synthetized because they are promising materials to improve nanoscale performance. However, little theoretical study has been carried out regarding the thermal stability of HEA NPs. Here, atomistic simulations have been conducted to study the thermal response of FeCuCrCoNi HEA NPs as a function of size. Atomistic modeling shows that melting point can be explained in terms of a two-phase model without the contribution of surface melting as is predicted through liquid shell models. On the other hand, it is observed that premelting starts with a preferential mobility of Fe and Cu atoms. Simulations show that due to the enhanced diffusion there is no evidence of precipitation or clustering during the thermal load, which is independent of the HEA NP size.