The application of thermo-rheological models to forecast active lava flow emplacement and quantify the eruptive parameters of older flow-producing eruptions has become a somewhat common tool over the last decade. With the modification and adaption of these models to modular computing languages, they are now easier, quicker, and being incorporated into studies of both terrestrial and planetary volcanism. These models, such as FLOWGO, rely on numerous assumptions and input parameters, some of which such as radiant emissivity are not well understood for molten materials. Without a well-grounded knowledge of how this parameter governs radiant cooling, physics-based estimates of temperature and models such as FLOWGO that track cooling with time will be in error. Here, we perform a detailed FLOWGO-based modeling study of lava flows emplaced at Tolbachik volcano during the 2012-2013 and the 1975-1976 eruptions. Specifically, we have modified the FLOWGO model to incorporate a two-component emissivity model linked to the fraction of molten lava and cooled crust. We focus first on the large Leningradskoye Flow emplaced at the start of the 2012 eruption, relying on data from numerous other orbital sensors including MODIS, ASTER and ALI to constrain some of the model input parameters. The two-component emissivity adaption produced better fits to the final flow length and was found to be most significant for flows with lower percentages of initial crust cover. We then applied these results and model constraints to the large Cone II flow formed in 1975, for which no satellite-based constraining data are available. By knowing the final flow dimensions coupled with the constraints determined from the previous modeling, we were able to estimate an effusion rate (700 m3/s), initial velocity (1.5 to 2 m/s) and final viscosity (108 Pa·s). Interestingly, a nearly identical model fit was achieved with a higher effusion rate (1250 m3/s) and correspondingly lower crust cover. In this scenario, modeling the two-component emissivity was critical for accurate model results. This represents the first study to implement two-component emissivity into thermo-rheological modeling of lava flows. The results show that this is an important factor for model accuracy and critical for large, higher effusion rate flows as well as for our understanding of older, “data-limited” flows on Earth and other planets.