  We describe the framework and strategy of the \^G infrared search for
extraterrestrial civilizations with large energy supplies, which will use the
wide-field infrared surveys of WISE and Spitzer to search for these
civilizations' waste heat. We develop a formalism for translating mid-infrared
photometry into quantitative upper limits on extraterrestrial energy supplies.
We discuss the likely sources of false positives, how dust can and will
contaminate our search, and prospects for distinguishing dust from alien waste
heat. We argue that galaxy-spanning civilizations may be easier to distinguish
from natural sources than circumstellar civilizations (i.e., Dyson spheres),
although Gaia will significantly improve our capability to identify the latter.
We present a "zeroth order" null result of our search based on the WISE all-sky
catalog: we show, for the first time, that Kardashev Type III civilizations (as
Kardashev originally defined them) are very rare in the local universe. More
sophisticated searches can extend our methodology to smaller waste heat
luminosities, and potentially entirely rule out (or detect) both Kardashev Type
III civilizations and new physics that allows for unlimited "free" energy
generation.
