This modeling study intended to solve a part of the global scientific problem related to increased concentrations of carbon dioxide in the atmosphere via emissions from terrestrial ecosystems that, along with anthropogenic emissions, make notable contributions to the processes of climate change on the planet. The main stream of CO2 from natural terrestrial ecosystems is related to the activation of biological processes, such as the production/destruction of plant biomass. In this study, the Wetland-DNDC computer simulation model with a focus on nitrogen and carbon biogeochemical cycles was used to study the effect of hydrothermal conditions on greenhouse gas fluxes in West Siberian peatlands. The study was implemented on the site of the world’s largest pristine wetland/peatland system, the Great Vasyugan Mire (GVM). The study was carried out based on data from permanent measurements at meteo stations and our own in situ measurements of hydrological and thermal parameters on sites, which allowed for testing different scenarios of changes in environmental conditions (temperature, precipitation, groundwater level) together with a change in GHG fluxes. The study revealed the air temperature and the level of groundwater as the main drivers controlling CO2 fluxes. The study of different scenarios of change in annual air temperature revealed the threshold of change in the wetland/peatland ecosystem from carbon sink to carbon source to the atmosphere to happen with an increase in the average annual air temperature by 3 °C with reference to the average annual air temperature values in 2019. Also, we found that the wetland/peatland ecosystem turned to act as an active carbon sink with about 7 cm increase in annual groundwater level, compared with its base level of −21 cm.