There isn't much detailed information for this online. Even the various manufacturers don't generally cite desired temperatures. Wikipedia says up to 480C/900F, but does not cite a source for this temperature. The NY Times says that a traditional charcoal tandoor gets up to 750F, but does not mention a source either. Homedoor, the one manufacturer who mentions a temperature, says that their units go up to 650F.
None of these sources mention a desired optimal temperature, though. It seems likely that the temperature would be similar to the optimal temperature for Neopolitan pizza, between 600F and 700F.
Also, a tandoor is designed so that the clay walls will be hotter than the air inside the oven -- I'd assume probably 50-100F hotter, but that's basically a blind guess as I can't find any measurements anywhere.
The one thing I can tell you from personal experience is that you cannot make Indian naan with the proper texture in a home oven with a pizza stone which only gets up to 525F. Believe me, I've tried.