Nanodiamond particles with typical diameters of 20 and 6 nm produced by high pressure high temperature or detonation processes have been studied by micro-Raman spectroscopy. We show that the frequency downshift and broadening of the first-order diamond phonon band is not uniquely related to phonon confinement, as commonly assumed. Local heating caused by the focused laser light must be also taken in account, since it may affect the Raman spectrum in a similar fashion, even at relatively low laser power levels. A combined theoretical model considering both effects (quantum confinement and local heating) on the excited phonon modes is presented and adopted for the simulation of the experimental data. We observe different heating behaviours upon laser illumination depending on the particles origin, thus underscoring the importance to compensate for this effect before retrieving structural parameters.