Numerical analysis of the heat balance at the flash event during flash sintering of granular ceramic nanoparticles was performed assuming continuum solid state as well as simultaneous surface softening/liquid formation and current percolation through the nanoparticle contacts. Assuming inter-particle radiations in the specimen volume, the electric Joule heat generated at the nanoparticle contacts partially lost by radiation from the specimen external surfaces. Considering the thermal effects due to rapid heating rate and free-molecular heat conduction regime, high-temperature gradients between the nanoparticle surfaces and the surrounding gas were developed. The attractive capillary forces, induced by the particle surface softening/liquid at the percolation threshold, lead to rapid rearrangement and densification of the nanoparticles. The excess Joule heat, already at the flash event, suffices the excess internal heat that is necessary for partial or full melting. Particle surface softening/liquid formation is a transient process, hence followed by crystallization immediate after the nanoparticle rearrangement. Thermal runaway is associated with local surface softening/melting and its solidification.