The thermal history of the Melut rift Basin was studied in a number of wells and along a northeast-southwest cross sectionacross the basin using 1-D and 2-D basin models. Modelling was conducted using PetroMod software to test subsidence, thermal history and their implications for hydrocarbon generation, migration and accumulations. Geotherms were found ranging between 24 and 44 °C/km and average 32 °C/km and present day heat flow was found to vary between 53 and 65 averaging 59 mW/m2. A geologicaly realistic paleoheat flow model with higher heat flow peaks of 75, 70 and 65 mW/m2 during the first, second and third rifting phases respectively, calibrated against vitrinite reflectance data was employed. The model was found sensitive to Cenozoic erosions and a 600 m of exhumation did support the vitrinite data in providing a reasonable fit in most locations. Using the Easy %Ro vitrinite kinetic model for maturity the average present day oil window was found between 1565 and 4050 m in the wells studied and between 1705 and 4200 m along the cross section. Using type-II kerogen for the Aptian-Albian source rocks, the hydrocarbon generation and expulsion were modelled and revealed that the generation started as early as 95 Ma in some areas but significant generation rates were during the second rifting phase and expulsion started at around 85 Ma. Calculations of the probable expelled amounts of hydrocarbon from the northern sub basin are high and up to 2.2 × 1011 bbls of oil and 2.3 × 1014 ft3of gas. Migration of oils from Cretaceous source rocks kitchen to the Cenozoic traps was probably through faults, porous carrier beds and breaching of traps cap rocks. The filling of these traps might be periodic during the rifting episodes and hydrocarbons remigrated from deeper traps to shallow ones. It is possible that thinner and siltier cap rocks along the hydrocarbon migration path, may have allowed gas to scape but holded the oil back. It is most probable that part of the hydrocarbons might have been generated from shallower source rocks areas and a 2-D hybrid Darcy-Flow path model have demonstrated this and predicted a number of accumulations which are similar to the known large discoveries such as Palogue-Fal and Adar-Yale oil fields.