This paper considers joint device activity detection and channel estimation in Internet of Things (IoT) networks, where a large number of IoT devices exist but merely a random subset of them become active for short-packet transmission at each time slot. In particular, to improve the detection performance, we propose to leverage the temporal correlation in user activity, i.e., a device active at the previous time slot is more likely to be still active at the current time slot. Despite the appealing temporal correlation feature, it is challenging to unveil the connection between the estimated activity pattern for the previous time slot (which may be imperfect) and the true activity pattern at the current time slot due to the unknown estimation error. In this paper, we manage to tackle this challenge under the framework of approximate message passing (AMP). Specifically, thanks to the state evolution, the correlation between the activity pattern estimated by AMP at the previous time slot and the real activity pattern at the previous and current time slot is quantified explicitly. Based on the well-defined temporal correlation, we further manage to embed this useful SI into the design of the minimum mean-squared error (MMSE) denoisers and log-likelihood ratio (LLR) test based activity detectors under the AMP framework. Theoretical comparison between the SI-aided AMP algorithm and its counterpart without utilizing temporal correlation is provided. Moreover, numerical results are given which show the significant gain in activity detection accuracy brought by the SI-aided algorithm.