Unfortunately i dont think you are going to be able to do it, unless, possibly, you run the unit so fierce, that the soot burns off.... but i cant think you would want to do that.
It might be worth trying though? Im thinking 6 or 700c ish. Cast glows at about those temps, but, obviously the temp of the firebox wont be the temp of the rest of it.
We have a solid fuel rayburn - run it hot, and the firebricks end up perfectly white - but then i guess there is still a small amount of white deposit - only very small though.