The wire is a black body.
Anything that absorbs all the radiant energy (heat and light), that strikes it, is a black body. Your black baseball cap on a hot summer day is a good example. All of the sunlight is absorbed by the cap. As it absorbs energy it heats up until it radiates as much energy as it absorbs.
The color of the light that is radiated does not depend on what the black body is made of but only on its temperature. A hot coil of wire and a star will radiate the same color of light if they are at the same temperature.
Your toaster and the sun have a lot in common!