This paper reports on the laser heating of nanoparticles (diameters $\leqslant 1$ μm) confined in a reactive plasma by short (150 ps) and intense ($\sim 63$ mJ) UV (355 nm) laser pulses (laser-induced incandescence, LII). Important parameters such as the particle temperature and radius follow from analysis of the emission spectrum of the heated nanoparticles. The nanoparticles are not ideal black bodies, which is taken into account by calculating their emissivity using a light-scattering theory relevant to our conditions (Mie theory). Three sets of refractive index data from the literature serve as model input. The obtained radii range between 100 and 165 nm, depending on the choice of refractive index data set. By fitting the temperature decay of the particles to a heat exchange model, the product of their mass density and specific heat is determined as $(1.3\pm 0.5)$ J K−1 cm−3, which is considerably smaller than the value for bulk graphite at the temperature our particles attain (3000 K): 4.8 J K−1 cm−3. The particle sizes obtained in situ with LII are compared with ex situ scanning electron microscopy analysis of collected particles. Quantitative assessment of the LII measurements is hampered by transport of particles in the plasma volume and the fact that LII probes locally, whereas the samples with collected particles have a more global character.