A nitrogen-vacancy (NV(-)) centre in a nanodiamond, levitated in high vacuum, has recently been proposed as a probe for demonstrating mesoscopic centre-of-mass superpositions and for testing quantum gravity. Here, we study the behaviour of optically levitated nanodiamonds containing NV(-) centres 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 ≈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(-) centre's spin coherence time. These values of T(i) make it clear that the diamond is not melting, contradicting a recent suggestion. Additionally, using the measured damping rate of a levitated nanoparticle at a given pressure, we propose a new way of determining its size.