Our response time (RT) to even a simple stimulus is highly variable, influenced by the temporal structures of both current and past trials. Part of this variation is traditionally explained as a covariation with hazard, the conditional probability that the stimulus will immediately occur. Here we aim to go beyond this descriptive explanation and, through behavioral experiments and computational modeling, to reveal the potentially rich, temporally dynamic computations underlying simple RTs. In Study 1, the assumed computations that best explain all the RT patterns not only consider the present (such as hazard), but also integrate probabilisitic information from the past (via accumulated activities and learning) and that from the future (via temporally discounted prospects). In Study 2, we find that even a self-initiated expectation of the future, despite its lack of support from real experiences, may influence the subsequent RT. Together, the two studies suggest that simple RTs may engage temporal computations that are far more sophisticated than widely assumed.