A model of the thermal evolution of the lithosphere of the West Siberian Basin in the area of Superdeep Well SG-6, which was drilled through the Koltogor–Urengoi graben, is used to numerically estimate the generation of various hydrocarbon (HC) fractions by the Triassic and Jurassic source rocks. The thermal model assumes the emplacement of a sill into the subsurface layers of the basement in the Early Jurassic and hydrothermal activity in the Late Pliocene–Lower Pleistocene, which noticeably impacted the conversion history of the HC potential of the Triassic and Jurassic source rocks. For the Triassic Pur formation, the emplacement of the sill into the subsurface layers of the basement in the Lower Jurassic drastically intensified the conversion of the HC potential to 84% and the degradation of more than 97% of the generated light oil mass. Calculations show that the heavy oil generated by the rocks of the Pur, Togur, and lower horizons of the Tyumen formations has degraded almost completely as a result of secondary cracking, while heavy oil predominates among the generated HC fractions in the upper horizons of the Tyumen Formation and in the rocks of the Bazhenovo Formation. The light oil remaining nowadays in the matrix of the source rocks has completely degraded in the Triassic rocks but makes up much of the HC products in rocks at the bottom of the Togur Formation and the top of the Tyumen Formation. This oil is the dominant in the upper horizons of the Togur Formation and in the bottom part of the Tyumen Formation. According to calculations, gas hydrocarbons account for a significant proportion of HC products in the Togur and Tyumen formations, and they dominate in the Middle Triassic Pur Formation. At the relatively low initial potential of HC generation and a low content of organic matter in the rocks of the Pur, Togur, and Tyumen formations, no primary expulsion threshold of liquid HC has been reached, and the generated liquid HC probably did not leave the rock matrix, while the gaseous HC likely migrated. The threshold of primary expulsion of liquid HC for the Bazhenov rocks was calculated to be reached at about 65 My.