Large open-plan compartment fires in modern buildings may exhibit a local burning region travelling across the floor plan as a ‘travelling fire’. This phenomenon has been found in the forensic investigations of fire accidents and in the large compartment fire tests. The fire impact in a large compartment is spatially non-uniform and time-variant, which can cause severe local damage to structural components. Advanced from the previous models assuming constant travelling, the natural fire model established in this paper comprises time-variant and test-based travelling behaviour models and localised fire models of various modes. It is demonstrated with the fast-spread Veselí fire test and the slow-spread Malveira fire test. A generic structural model is set up within OpenSees for fire to examine the thermal impact on structural members under various travelling fire scenarios of different travelling parameters, fire travelling directions, and beam sizes. Locally much higher thermal responses are represented after introducing behaviour models while adopting the same design fire load. Based on the work in this paper, a library of design fire models can be potentially enabled to examine the fire safety performance of structures regarding the realistic fire load and fire impact aiming for discovering unknown worse fire scenarios.