Human cognition is marked by the ability to explain patterns in the world in terms of variables and regularities that are not directly observable, e.g., mental states, natural laws and causal relationships. Previous research has demonstrated a capacity for inferring hidden causes from covariational evidence, as well as the use of temporal information to identify causal relationships. Here we explore the human ability to use temporal information to make inferences about hidden causes, causal cycles, and other causal relationships, without relying on interventions. We examine two behavioral experiments and compare participants' judgments to those of Bayesian computational-level models that make use of temporal order and delay information to infer the causal structure behind observed events. Participants were able to use order and timing information to discover hidden causes, and to make inferences about causal structures relating hidden and observable variables.