Not at all wavelengths. An object of finite size and infinite temperature can produce all the wavelengths, but the probability of it generating, say visible light is really low approaching 0. So you can think about the relative number of visible photons you could observe and that gives you a color.
My gripe with this is that if our understanding of quantum mechanics and general relativity is correct there is a limit of temperature. When a photon has a wavelength equal or smaller than the Planck length said photon contains enough energy to create a black hole. So, the upper limit of temperature should be the point at which the generation of black holes dominates the spectrum.
My gripe with this is that if our understanding of quantum mechanics and general relativity is correct there is a limit of temperature. When a photon has a wavelength equal or smaller than the Planck length said photon contains enough energy to create a black hole. So, the upper limit of temperature should be the point at which the generation of black holes dominates the spectrum.