Magma emplacement in organic‐rich sedimentary basins is a main driver of past environmental crises. Using a 2‐D numerical model, we investigate the process of thermal cracking in contact aureoles of cooling sills and subsequent transport and emission of thermogenic methane by hydrothermal fluids. Our model includes a Mohr‐Coulomb failure criterion to initiate hydrofracturing and a dynamic porosity/permeability. We investigate the Karoo Basin, taking into account host‐rock material properties from borehole data, realistic total organic carbon content, and different sill geometries. Consistent with geological observations, we find that thermal plumes quickly rise at the edges of saucer‐shaped sills, guided along vertically fractured high‐permeability pathways. Contrastingly, less focused and slower plumes rise from the edges and the central part of flat‐lying sills. Using a novel upscaling method based on sill‐to‐sediment ratio, we find that degassing of the Karoo Basin occurred in two distinct phases during magma invasion. Rapid degassing triggered by sills emplaced within the top 1.5 km emitted ~1.6·103 Gt of thermogenic methane, while thermal plumes originating from deeper sills, carrying a 13‐times‐greater mass of methane, may not reach the surface. We suggest that these large quantities of methane could be remobilized by the heat provided by neighboring sills. We conclude that the Karoo large igneous province may have emitted as much as ~22.3·103 Gt of thermogenic methane in the half million years of magmatic activity, with emissions up to 3 Gt/year. This quantity of methane and the emission rates can explain the negative δ13C excursion of the Toarcian environmental crisis.