The paper introduces and investigates relational temporal machine (RTM) as a general abstract model for generic temporal querying. The RTM devices subsume most temporal query languages that have emerged in the literature. A first contribution of the paper is to provide two simplified forms for our machines, namely extended onetape RTMs and one-tape RTMs. Another contribution is to establish connections between RTMs and the T-WHILE and TS-WHILE extensions of FO based on complexity criteria.