With the reflection of nearly all types of social cultural, societal and everyday processes of our lives in the web, web archives from organizations such as the Internet Archive have the potential of becoming huge gold-mines for temporal content analytics of many kinds (e.g., on politics, social issues, economics or media). First hand evidences for such processes are of great benefit for expert users such as journalists, economists, historians, etc. However, searching in this unique longitudinal collection of huge redundancy (pages of near-identical content are crawled all over again) is completely different from searching over the web. In this work, we present our first study of mining the temporal dynamics of subtopics by leveraging the value of anchor text along the time dimension of the enormous web archives. This task is especially useful for one important ranking problem in the web archive context, the time-aware search result diversification. Due to the time uncertainty (the lagging nature and unpredicted behavior of the crawlers), identifying the trending periods for such temporal subtopics relying solely on the timestamp annotations of the web archive (i.e., crawling times) is extremely difficult. We introduce a brute-force approach to detect a time-reliable sub-collection and propose a method to leverage them for relevant time mining of subtopics. This is empirically found effective in solving the problem.