When physicists say something is true in the infrared limit, they mean that it is true for low enough wavelengths. In this case the exact definition of "low enough" depends on the temperature. If the temperature is high enough, then that set of "low enough" wavelengths will include the entire visible part of the spectrum. So as T goes to infinity, the light that we can actually see will get brighter and brighter, but the relative power emitted at different wavelengths will stay the same, so the colour will stay the same. But that's just in the visible region. There will be higher and higher frequency x rays and gamma rays emitted, eventually to the point of being lethal to a human observer.