Given two topics of interest (A and C) that are otherwise disconnected - for instance two concepts: a disease ("Migraine") and a therapeutic substance ("Magnesium") - this paper attempts to find the conceptual bridges (e.g., serotonin (B)) that connects them in a meaningful way. This problem of mining implicit linkage is known as hypotheses generation and its potential to accelerate scientific progress is widely recognized. Almost all of the prior studies to tackle this problem ignore the temporal dynamics of concepts. This is limiting because it is known that the semantic meaning of a concept evolves over time. To overcome this issue, in this study, we define this problem as mining time-aware Top-k conceptual bridges, and in doing so provide a systematic approach to formalize the problem. Specifically, the proposed model first extracts relevant entities from the corpus, represents them in time-specific latent spaces, and then further reasons upon it to generate novel and experimentally testable hypotheses. The key challenge in this approach is to learn a mapping function that encodes the temporal characteristics of concepts and aligns the across-time latent spaces. To solve this, we propose an effective algorithm that learns precise mapping sensitive to both global and local semantics of the input query. Both qualitative and quantitative evaluations performed on the largest available biomedical corpus substantiate the importance of leveraging temporal dynamics and suggests that the generated hypotheses are novel and worthy of clinical trials.