Using molecular dynamics simulations and theoretical analysis we study heat flow and phase behavior at the interface between high power-density, nanoscale heat sources and an embedding fluid medium. We show that the fluid next to the nanoparticle can be heated well above its boiling point without a phase change. Under increasing nanoparticle temperature, the heat flux saturates, which is in sharp contrast with the case of flat interfaces, where a critical heat flux is observed followed by development of a vapor layer and heat flux drop. These differences in heat transfer are explained by the curvature-induced pressure close to the nanoparticle, which inhibits boiling. We observe similar behavior for water, organic fluid, as well as generic model fluid underscoring generality of the results. We will also discuss the limits of the spatial and temporal localization of extreme temperature excursions and the limits to the applicability of the linear response theory to heat transfer at extremely large heat fluxes.