Recently I have become interested in black-body radiation. I knew of this and color temperature, but I didn't quite understand any of it. I admit I'm still learning. I've thought about the Sun's photosphere being white, rather than yellow, and wondered that if the temperature of the photosphere could be determined by black-body radiation or color temperature, could this be applied to a nuclear explosion?
Yes it can, but just as with the Sun, you only get to measure the temperature of what you can see: the temperature in the centre of the explosion may be much higher, and I suppose needs to be calculated based on models of what is going on.
In fact, the gamma radiation and x-ray radiation produced in a nuclear explosion is black-body gamma radiation.
What happens is that for a very short time during expanding shell-phase of the detonation, the exploding matter is several million Kelvin hot which corresponds to a temperature radiating in those very short-wavelength regimes.
As the exploding matter is still very dense, the thermal relaxation timescale is much shorter than the expansion timescale, and thus the high energy radiation can thermalize, which produces a black body.