Sources of methane to sedimentary environments are commonly identified and quantified using the stable isotopic compositions of methane. The methane "clumped-isotope geothermometer", based on the measurement of multiply substituted methane isotopologues (13CH3D and 12CH2D2), shows promise in adding new constraints to the sources and formational environments of both biogenic and thermogenic methane. However, questions remain about how this geothermometer behaves in systems with mixtures of biogenic and thermogenic gases and different biogenic environments. We have applied the methane clumped-isotope thermometer to a mixed biogenic-thermogenic system (Antrim Shale, USA) and to biogenic gas from gas seeps (Santa Barbara and Santa Monica Basin, USA), a pond on the Caltech campus, and methanogens grown in pure culture. We demonstrate that clumped-isotope based temperatures add new quantitative constraints to the relative amounts of biogenic vs. thermogenic gases in the Antrim Shale indicating a larger proportion (~50%) of thermogenic gas in the system than previously thought. Additionally, we find that the clumped-isotope temperature of biogenic methane appears related to the environmental settings in which the gas forms. In systems where methane generation rates appear to be slow (e.g., the Antrim Shale and gas seeps), microbial methane forms in or near both internal isotopic equilibrium and hydrogen-isotope equilibrium with environmental waters. In systems where methane forms rapidly, microbial methane is neither in internal isotopic equilibrium nor hydrogen-isotope equilibrium with environmental waters. A quantitative model of microbial methanogenesis that incorporates isotopes is proposed to explain these results.