Recent experimental evidence suggests that the perception of temporal intervals is influenced by the temporal context in which they are presented. A longstanding example is the time-order-error, wherein the perception of two intervals relative to one another is influenced by the order in which they are presented. Here, we test whether the perception of temporal intervals in an absolute judgment task is influenced by the preceding temporal context. Human subjects participated in a temporal bisection task with no anchor durations (partition method). Intervals were demarcated by a Gaussian blob (visual condition) or burst of white noise (auditory condition) that persisted for one of seven logarithmically spaced sub-second intervals. Crucially, the order in which stimuli were presented was first-order counterbalanced, allowing us to measure the carryover effect of every successive combination of intervals. The results demonstrated a number of distinct findings. First, the perception of each interval was biased by the prior response, such that each interval was judged similarly to the preceding trial. Second, the perception of each interval was also influenced by the prior interval, such that perceived duration shifted away from the preceding interval. Additionally, the effect of decision bias was larger for visual intervals, whereas auditory intervals engendered greater perceptual carryover. We quantified these effects by designing a biologically-inspired computational model that measures noisy representations of time against an adaptive memory prior while simultaneously accounting for uncertainty, consistent with a Bayesian heuristic. We found that our model could account for all of the effects observed in human data. Additionally, our model could only accommodate both carryover effects when uncertainty and memory were calculated separately, suggesting separate neural representations for each. These findings demonstrate that time is susceptible to similar carryover effects as other basic stimulus attributes, and that the brain rapidly adapts to temporal context.