Today I learned what color an infinitely hot black body would have.
While the amount of energy in the shorter wavelengths would increase without bound, basically resulting in an ultraviolet catastrophe,1 we can only perceive wavelengths within the visible spectrum, and what we perceive has less red and more blue light. By taking into account how we perceive color, we would perceive a somewhat bluish color.
When an object is sufficiently hot, the light it emits in visible wavelengths would approximate the visible light for infinitely hot objects, even if it is still very different for very short non-visible wavelengths. This means if we looked at extremely hot objects such as a young neutron star,2 they would have a color like this! When the universe was much hotter when it was very young, it would have also had this color.
The accretion disk around a black hole is also very hot, and we would be surrounded by this color if we were to be stuck inside swirling along inside the disk, but outside it would be very different because of both Doppler and gravitational red or blue shift. Of course, we would have bigger problems if we were stuck inside the accretion disk around a black hole, since we would be vaporized due to the extreme heat.
The ultraviolet catastrophe means there is an infinite amount of energy, which makes no sense for bodies with finite temperatures, but does make sense for bodies with infinite temperatures.↩︎
And in terms of what color we would perceive, not enough time has passed since the Big Bang such that no neutron star would have cooled down enough to count as old for this purpose.↩︎