To describe the temporal behavior of laser-induced incandescence (LII) signals emitted from nanoparticles in atmospheric flames or low-pressure processing plasmas, we derive two analytic formulae in detail from the energy balance equation of nanoparticles heated by laser pulses. We demonstrate quantitative size monitoring by observing Si nanoparticles growing in an argon plasma diluted with 5% SiH4 at a pressure of 20 mTorr, using the LII technique. In this experiment, it is found that the signal-to-noise ratio of the LII signal is sufficient to allow the identification of particles larger than 10 nm in diameter with a measurement uncertainty that is estimated to be less than 5%.