Yeah, from what i've read, under normal pressures, carbon won't even melt, it will just directly go to burning at 3,550 celcius. And as diamond is an allotrope of carbon, i think this applies to it as well.

EDIT: quoting wikiepdia - "Carbon also has the highest sublimation point of all elements. At atmospheric pressure it has no melting point as its triple point is at 10.8 ± 0.2 MPa and 4,600 ± 300 K (~4,330 °C or 7,820 °F), so it sublimes at about 3,900 K".