  A nitrogen-vacancy (NV$^-$) center in a nanodiamond, levitated in high
vacuum, has recently been proposed as a probe for demonstrating mesoscopic
center-of-mass superpositions \cite{Scala2013, Zhang2013} and for testing
quantum gravity \cite{Albrecht2014}. Here, we study the behavior of optically
levitated nanodiamonds containing NV$^-$ centers at sub-atmospheric pressures
and show that while they burn in air, this can be prevented by replacing the
air with nitrogen. However, in nitrogen the nanodiamonds graphitize below
$\approx 10$ mB. Exploiting the Brownian motion of a levitated nanodiamond, we
extract its internal temperature ($T_i$) and find that it would be detrimental
to the NV$^-$ center's spin coherence time \cite{Toyli2012}. These values of
$T_i$ make it clear that the diamond is not melting, contradicting a recent
suggestion \cite{Neukirch2015}. Additionally, using the measured damping rate
of a levitated nanoparticle at a given pressure, we propose a new way of
determining its size.
