"Red Hot" Objects & the Ultraviolet Catastrophe

As you say, Rayleigh-Jeans law did not adequately explain observations made at the time. However, it still had merits. It was derived from a very simple classical argument (rather than being an ad hoc formula fitted to observations) and it had the correct asymptotic behavior for long wavelengths.

Formulas derived from a simpler more fundamental theory are generally preferred in physics, and the correct asymptotic behavior was an indication that this attempt was on the right track, even though something was obviously missing.

I'm unsure about the proper history here, but what you should take away from the Rayleigh - James example is that it fail miserably to account for the spectral features of hot objects.

The 'ultraviolet catastrophie' means -- as you say -- that more energy will be radiated away at increasingly shorter wave-lengths. This catastrophe is so bad (i think it makes the spectrum non-normalizable) that asking questions regarding winch particular colour a hot object has becomes irrelevant.

Basically, you have bigger problems to worry about.

Rayleigh himself notice that his formula gave infinte energy when integrating over all frequencies so he proposed an ad hoc exponential decay to his energy density for large frequencies.

In Rayleigh own words

If we introduce an exponential factor, the complete expression will be $$c_1\theta k^2 e^{-c_2k/\theta}.$$ Whether this represents the facts of observation I am not in a position to say. It is to be hoped that the question may soon receive an answer at the hands of the distinguished experimenters who have been occupied with this subject.

Note: $\theta$ and $k$ stand for absolute temperature and frequency, respectively. The constants $c_1$ and $c_2$ are phenomenological parameters.