I'm not sure if this will help you, but the (local) interstellar
radiation field has been measured and modeled by various groups.  If I
remember things correctly, the models involved contributions from three
different BB sources, so there's no obvious "temperature" of background
radiation in our local area.  However, the following references give the
interstellar radiation density as a function of wavelength, and you can
integrate and average in an appropriate manner to get an "effective"
temperature if you like:

Witt and Johnson (1973) Astrophys. J. 181, 363 - 368
Henry et al. (1980) Astrophys. J. 239, 859 - 866
Mathis et al. (1983) Astron. Astrophys. 128, 212 - 229

As you can see, the references are out of date, but they might get you
started.

Hope this helps,