In steady state, the net radiation emitted from the wires can be used to describe its temperature. Maybe a way to say that is, nature already accounts for these effects if you turn the toaster on for an appreciable amount of time.
I'd also question the physics of that claim. I'm assuming you are using Wien's displacement law and backing out a temperature from the wavelength associated with orange light? Your math is a little off since I get around 5000K (about the surface temp of the Sun, 20,000K would get you in the UV). This would be correct if you assume that 1.) the object in question is a blackbody and 2.) orange is actually its spectral emissive peak. But 1.) your wire is not a blackbody and 2.) just because the wires appear to glow orange to your eyes does not mean its blackbody peak emission wavelength is exactly orange (or even in the visible, it is most likely in the infrared, as with most commonly occurring things on Earth). Technically you would need some detector that can find the emitted power as a function of wavelength, and scan through the appropriate range of wavelengths. In other words, your eye is not a good detector for characterizing the temperature of a surface via this type of thermal radiation detection.
And I think to respond to the OP, as many have said, It is a "short," per se, since you have current running through a fairly good conductor. You can't have an ideal "short" unless you have a superconductor. But in this case, your application is to generate heat via Joule heating. So you run high current through high effective resistance. What is the problem?
You can approximate any electronic configuration as an ideal linear (i.e., LRC or higher related derivatives) circuit, the correctness of the approximation depending on the situation. In this case, the current flow through any wire can be well approximated by some choice values of R, L, C, or higher derivative terms. In the ideal short would then mean infinite current which means, if the circuit is undriven, it lasts an infinitesimal amount of time, as the potential would equalize immediately, this is the limit of the ideal conductor.