Our idea of "warm" colors is just a historical accident. Wood burns orange because it produces soot, which glows orange in the flame. Same applies to candles too, because there’s never enough oxygen to burn all the carbon.
If we’d started with purified hydrocarbons instead, blue might have been the ultimate "warm" color. Natural gas burns with a blue or even invisible flame, a sign of complete combustion. Orange, then, would be the color of flawed, struggling fire.
Imagine a house heated and lit by a gas furnace instead of a traditional fireplace. The light from the fire would be blue, and we’d associate that glow with warmth and coziness. Picture old paintings with a cozy atmosphere, their hearths glowing blue. If everyone grew up like that, blue would be the warmest color instead of orange.
"Different flame types of a Bunsen burner depend on oxygen supply. On the left a rich fuel with no premixed oxygen produces a yellow sooty diffusion flame; on the right a lean fully oxygen premixed flame produces no soot and the flame color is produced by molecular radicals, especially CH and C2 band emission."
Source: Wikipedia
I think you're missing the point a bit. I'm talking about how much heat different wavelengths of light transfer.
There's an interesting experiment you can do if you have the right equipment: take the classic experiment where you produce a rainbow with a prism. Then, take a sensitive thermometer and go along the spectrum. The red end of the spectrum will be the warmest (unless you go even further, the area beyond that will be even warmer from the infrared), the blue end the coldest (although still warmer than the surroundings).
Oh ok. So when the peak of the emission spectrum is in the IR range, the visible color will definitely be closer to red or orange. The amount of blue light emitted in that case will be very low. That's what the thermometer experiment can definitely demonstrate clearly.
However, if the black body is hot enough that the peak is in the blue wavelength band, then the total IR output should also be pretty high, just like everything else is at that point. I wonder if it's even higher than in the first example. Would need to calculate that properly... Anyway there will also be a fair bit of UV, so don't try this at home. Maybe even some x-rays if the arc is hot enough.
As far as traditional carbon-arc lamps are concerned, people at the time wrote that the light was white. Maybe the arc was not hot enough or be perceived as blue. Also, the human eye is not particularly sensitive at those wavelengths, so that could explain some of it too.