Nonlinear and time-varying distributed parameter systems (DPSs) are challenging to accurately model due to potential spatiotemporal coupling, infinite-dimensional property, and time-varying dynamics. Although the least-squares support vector machine (LS-SVM) can effectively model lumped parameter systems, it is less effective to model the time-varying dynamics of a DPS, as it lacks the ability to incorporate time-varying spatiotemporal dynamics. Here, an online spatiotemporal LS-SUM approach is proposed to model a nonlinear and time-varying DPS. An adaptive spatial kernel function is first developed for online capture of the time-varying relationship between spatial locations. An online time coefficient model is then constructed to account for the time-varying temporal dynamics of the DPS. Combination of the adaptive spatial kernel function with the online time coefficient model allows for reconstruction of the complex DPS and ensures the model can reflect real-time spatiotemporal dynamics well. Experiments on a laboratory curing thermal process show the effectiveness of the proposed method.