Effects of a different CMBR temperature?

[rknop]

Use Wein's Law to figure out where the peak wavelength is. If it's not very close to or within a band where you're detecting things, then it probably won't matter much.

The intensity is going to scale as T^4, which is a lot -- but, even still, it's not very bright right now. Remember that to detect it, we have to use balloon-borne or space-based experiments, and even then there's a lot of other background and such to subtract.

What kinds of things are you trying to detect? With an example, I could probably give a back-of-the-napkin estimate of how much hotter the CMB would need to be for it to make a difference.

Also, it wouldn't change how we calculate blackbodies. The CMB may be our most perfect example of a blackbody, but the constants used (k and h) are measured in other places. I have a vague memory of the ultimate calibration of blackbodies coming from an experiment done at some observatory with molten platinum....