Apatite fission track analysis of 44 surface and borehole samples indicates that the Papuan Fold Belt was uplifted, eroded and cooled from the earliest Pliocene (5 Ma) to the present day. Uplift and cooling of basement in the Kubor and Muller Anticlines, 250 km apart, took place at 4.0±0.5 Ma, but thrusting of the large anticlines at the mountain front was probably within the last 1 Ma. This timing casts doubt on tectonic models requiring ongoing compression in the Miocene and favours a model with Late Miocene collision of New Guinea with an island arc to the north. The Mesozoic section in the western fold belt was heated to ≫100°C in the Pliocene, so is only prospective for gas and condensate, but the eastern fold belt had maximum palaeotemperatures at least 20°C lower, hence it is prospective for oil. A northeast‐southwest structural lineament is inferred to separate the western and eastern provinces. Mountain front anticlines, such as Iehi, underwent considerable heating in the Late Cretaceous, prior to Palaeocene uplift and erosion associated with opening of the Coral Sea. Pliocene heating was negligible in comparison. Any oil generation in the frontal anticlines would have been in the Late Cretaceous. This is likely to be true throughout the Fly Platform to the southwest, but in the fold belt hydrocarbons were generated during deep burial in the Pliocene. Thermal modelling of the Iehi 1 well indicates ∼ 800 m of Late Cretaceous eroded in the Palaeocene. Modelling of other fission track data suggests the presence of Late Jurassic and Early Cretaceous volcanogenic sediments in the fold belt.