To analyze transverse fire protection, the distribution law and evolution mechanism of transverse heat transfer during fire in utility tunnels is required urgently. In this study, the experiment and numerical simulation were employed to investigate the evolution of transverse heat transfer under the curved ceiling. After validation, the fire dynamics simulation models with unstructured geometry were established to predict the transverse heat flux. Through the experiment and simulation, the fire source and target location under the curved ceiling were considered, and the prediction models of heat flux provided by the flame body before the impingement point and the heat flux provided by the extension flame body and thermal environment were proposed. Based on the proposed models, the shift relationship (competition mechanism) between the components provided by flame body before the impingement point and the extension flame body (including the thermal environment) under the curved ceiling was illustrated. The transverse heat flux attenuation of each component in different fire scenarios with different fire sources and target point locations was compared to reveal the competition mechanism among the components in the heat flux. This work provides a reference for the transverse fire protection design and risk assessment in utility tunnels.