Composite structures have been employed in a variety of applications such as aerospace, automotive, et al. As a vital stage of composites manufacturing, curing involves complex physical and chemical behaviours and plays a significant role in the final mechanical properties and dimensional accuracy of the manufactured product. Modelling the curing process, especially the real temperature history, is necessary for the optimisation of cure cycles during composites manufacturing. Since thermochemical analysis using Finite Element (FE) simulations requires heavy computational loads and data-driven approaches suffer from the complexity of high-dimensional mapping. This paper proposes a physics-guided neural operator to directly predict the high-dimensional temperature history from the given cure cycle. By integrating domain knowledge into a time-resolution independent parameterised neural network, the mapping between cure cycles to temperature histories can be learned using a limited number of labelled data. Besides, a novel Fourier residual mapping is designed based on mode decomposition to accelerate the training and significantly boost the performance. Detailed experiments in several cases show that the proposed model can predict the temperature histories accurately and also can provide better process optimisation results.