Okay, we've seen the super hot Wolf-Rayet stars, especially WR 102 and 142, and the "slash stars," many of which are early O (O2-4.5/WN). We know the temperatures of these Wolf Rayet stars. So if we know that, what would their spectral types be in the standard Morgan-Keenan spectral classification (i.e. O2V or B0Ia+), and are there known stars with spectral class earlier than O2?
This is what Wikipedia says about it:
When the MKK classification scheme was first described in 1943, the only subtypes of class O used were O5 to O9.5. The MKK scheme was extended to O9.7 in 1971 and O4 in 1978, and new classification schemes that add types O2, O3, and O3.5 have subsequently been introduced.
It references the paper A New Spectral Classification System for the Earliest O Stars: Definition of Type O2
Thus, a new earliest spectral type has been defined.
So unless that information is outdated, there's no such thing as O1 or O0.
I don't believe that O0 is a real classification(see this chart), but if it were following the temperature steps it would probably be around 80,000-90,000 degrees Kelvin. The hottest star we know of is WR 102, which is 210,000 degrees Kelvin, and that is much, much hotter than my predicted O0 temperature. So the short answer is yes, O0 temperature stars exist, but O0 isn't truly a real classification. (The hottest real classification is O2, at 53,000 Kelvin and up) Hope I helped!
Edit: I forgot to add a closing parentheses and my Markdown was messed up Edit 2: I was looking at an outdated document, the real hottest classification is O2 not O3.