This is the color of something infinitely hot. Of course you’d instantly be fried by gamma rays of arbitrarily high frequency, but this would be its spectrum in the visible range.
This is also the color of a typical neutron star. They’re so hot they look the same.
It’s also the color of the early Universe!
This was worked out by David Madore.
As a blackbody gets hotter and hotter, its spectrum approaches the classical Rayleigh–Jeans law. That is, its true spectrum as given by the Planck law approaches the classical prediction over a larger and larger range of frequencies.
So, for an extremely hot blackbody, the spectrum of light we can actually see with our eyes is governed by the Rayleigh–Jeans law. This law says the color doesn’t depend on the temperature: only the brightness does!
And this color is shown above.
This involves human perception, not just straight physics. So David Madore needed to work out the response of the human eye to the Rayleigh–Jeans spectrum — “by integrating the spectrum against the CIE XYZ matching functions and using the definition of the sRGB color space.”
The color he got is sRGB(148,177,255). And according to the experts who sip latte all day and make up names for colors, this color is called ‘Perano’.
Here is some background material Madore wrote on colors and visual perception. It doesn’t include the whole calculation that leads to this particular color, so somebody should check it, but it should help you understand how to convert the blackbody spectrum at a particular temperature into an sRGB color:
• David Madore, Colors and colorimetry.
In the comments you can see that Thomas Mansencal redid the calculation and got a slightly different color: sRGB(154,181,255). It looks quite similar to me: