I wonder how you want to calculate a temperature if you already have a temperature. For the first part of your question: Check out how they calculate the cosmic background (2.7 K) temperature from the microwave spectrum.
I think Wien's Law is what you want here. Wiki has a page on it. If you are sure that the radiating object can be treated as a black body then all the formulae for visible light should work for lower frequency parts of the spectrum. The peak frequency of the radiation should yield the temperature. Have you the facility to plot the spectrum of your source around the peak? You may need to eliminate sources of microwave interference and a spectrum could reveal their presence.