We Use Non-Equilibrium Molecular Dynamics Simulations to Study the Heat Transfer Around Intensely Heated Solid Nanoparticles Immersed in a Model Lennard-Jones Fluid. We Focus Our Studies on the Role of the Nanoparticle Curvature on the Liquid Phase Stability under Steady-State Heating. for Small Nanoparticles We Observe a Stable Liquid Phase Near the Nanoparticle Surface, Which Can Be at a Temperature Well above the Boiling Point. Furthermore, for Particles with Radius Smaller Than a Critical Radius of 2 Nm We Do Not Observe Formation of Vapor Even above the Critical Temperature. Instead, We Report the Existence of a Stable Fluid Region with a Density Much Larger Than that of the Vapor Phase. We Explain the Stability in Terms of the Laplace Pressure Associated with the Formation of a Vapor Nanocavity and the Associated Effect on the Gibbs Free Energy. © 2014 AIP Publishing LLC.