LiDAR perception for autonomous driving applications offers highly accurate scene depiction in three-dimensional (3D) spaces, whose most representative task is LiDAR panoptic segmentation (LPS), as it offers exhibition of both instance- and semantic-level segmentation in a holistic manner. Although previous approaches have achieved mature performance, no research has explored temporal information for enhancing LPS performance. As multi-frame processing can assist in better predictions in terms of feature representation and recursive forecasting, which has been proven in other LiDAR perception challenges, this study proposes an effective and temporal-aware panoptic segmentation method for LiDAR point clouds. Specifically, we introduce two modules: convolution-based cross-frame fusion attention (CFFA) and adjacent shifted feature encoder (ASFE) modules. The CFFA module can fuse multi-frame features on the basis of the idea of convolution-based attention, whereas the ASFE module leverages adjacent model outputs and serves as an intermediate guide for final segmentation predictions. Consequent to our extensive experiments, the two modules have been reaffirmed in terms of their productivity in the realm of the LPS. The proposed LPS model achieves impressive panoptic-quality metric scores that are evaluated on different popular benchmarks (63.36% under SemanticKITTI and 78.54% under Panoptic nuScenes), outperforming previous state-of-the-art methods by a significant margin. Further quantitative and qualitative analyses provide evidence of the advantages of multi-frame processing for the LPS together with demonstrations of its particular behavior under different settings.