Nanodiamonds have emerged as promising materials for quantum computing, biolabeling, and sensing due to their ability to host color centers with remarkable photostability and long spincoherence times at room temperature. Recently, a bottom-up, high-pressure, high-temperature (HPHT) approach was demonstrated for growing nanodiamonds with color centers from amorphous carbon precursors in a laser-heated diamond anvil cell (LH-DAC) that was supported by a near-hydrostatic noble gas pressure medium. However, a detailed understanding of the photothermal heating and its effect on diamond growth, including the phase conversion conditions and the temperature-dependence of color center formation, has not been reported. In this work, we measure blackbody radiation during LH-DAC synthesis of nanodiamond from carbon aerogel to examine these temperature-dependent effects. Blackbody temperature measurements suggest that nanodiamond growth can occur at 16.3 GPa and 1800 K. We use Mie theory and analytical heat transport to develop a predictive photothermal heating model. This model demonstrates that melting the noble gas pressure medium during laser heating decreases the local thermal conductivity to drive a high spatial resolution of phase conversion to diamond. Finally, we observe a temperature-dependent formation of nitrogen vacancy centers and interpret this phenomenon in the context of HPHT carbon vacancy diffusion using CBΩ theory.