Bacteria that can live in extreme temperatures are called thermophiles (thermo = temperature, phile = love... so the word means to love temperature). They are a type of extremophile, or organisms that live in extreme conditions. Another example of an extremophile is a halophile (organisms that live in very salty conditions). Methanogens live in areas in which there is a lot of methane produced from anaerobic respiration.
These organisms are a part of the kingdom Archaebacteria (otherwise known as just "Archaea"), which consists of bacteria. As their name implies, archaebacteria live in environments in which there is very little oxygen. This, archaebacteria undergo anaerobic respiration. This is a characteristic that allows such organisms to live in the harsh conditions in which they are found.
I hope this helps! :)