A knowledge hypergraph is a form of heterogeneous graph representing the real world through $n$-ary relations, but existing knowledge hypergraphs are usually incomplete in both general and vertical domains. Therefore, it is challenging to infer the missing links from the existing links in knowledge hypergraphs. Most of the current studies employ knowledge representation learning methods based on $n$-ary relations to accomplish link prediction in knowledge hypergraphs, but they only learn the embedding vectors of entities and relations from time-unknown hyperedges without considering the influence of temporal factors on the dynamic evolution of facts, which results in poor prediction performance in dynamic environments. Firstly, based on the definition of temporal knowledge hypergraphs proposed by this paper for the first time, this paper puts forward a link prediction model for temporal knowledge hypergraphs and learns static and dynamic representations of entities from their roles, positions, and timestamps of temporal hyperedges. Then these representations 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. Meanwhile, it is theoretically proven that the proposed model is fully expressive with linear space complexity. Additionally, 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 link prediction tasks on the temporal knowledge hypergraph dataset.