Stemming from traditional knowledge graphs (KGs), hyper-relational KGs (HKGs) provide additional key-value pairs (i.e., qualifiers) for each KG fact that help to better restrict the fact validity. In recent years, there has been an increasing interest in studying graph reasoning over HKGs. In the meantime, due to the ever-evolving nature of world knowledge, extensive parallel works have been focusing on reasoning over temporal KGs (TKGs), where each TKG fact can be viewed as a KG fact coupled with a timestamp (or time period) specifying its time validity. The existing HKG reasoning approaches do not consider temporal information because it is not explicitly specified in previous benchmark datasets. Besides, all the previous TKG reasoning methods only lay emphasis on temporal reasoning and have no way to learn from qualifiers. To this end, we aim to fill the gap between TKG reasoning and HKG reasoning. We develop two new benchmark hyper-relational TKG (HTKG) datasets, i.e., Wiki-hy and YAGO-hy, and propose a HTKG reasoning model that efficiently models both temporal facts and qualifiers. We further exploit additional time-invariant relational knowledge from the Wikidata knowledge base and study its effectiveness in HTKG reasoning. Time-invariant relational knowledge serves as the knowledge that remains unchanged in time (e.g., Sasha Obama is the child of Barack Obama), and it has never been fully explored in previous TKG reasoning benchmarks and approaches. Experimental results show that our model substantially outperforms previous related methods on HTKG link prediction and can be enhanced by jointly leveraging both temporal and time-invariant relational knowledge.