A knowledge hypergraph is a form of a heterogeneous graph that represents the real world through n-ary relations. However, both in general and specific domains, existing knowledge hypergraphs often suffer from incompleteness. Therefore, it is a challenging task to reason the missing links through the existing links in the knowledge hypergraph. Currently, most research employs knowledge representation learning methods based on n-ary relations to carry out link prediction tasks in knowledge hypergraphs. However, these methods only learn embedding vectors of entities and relations from hyperedges with unknown temporal information, neglecting the impact of temporal factors on the dynamic evolution of facts, resulting in poor predictive performance in dynamic environments. Firstly, based on the definition of temporal knowledge hypergraph that proposed by this study for the first time, a link prediction model is proposed for temporal knowledge hypergraphs. Simultaneously, static and dynamic representations of entities are learnt from their roles, positions, and timestamps of temporal hyperedges, which are merged in a certain proportion and utilized as final entity embedding vectors for link prediction tasks to realize the full exploitation of hyperedge temporal information. At the same time, it is theoretically proved that the proposed model is fully expressive and has linear space complexity. In addition, a temporal knowledge hypergraph dataset CB67 is constructed from the public business data of listed companies, and a large number of experimental evaluations are conducted on this dataset. The experimental results show that the proposed model can effectively perform the link prediction task on the temporal knowledge hypergraph dataset.