Gradual emerging patterns (GEPs) are gradual item sets that occur less frequently in one data set and more frequently in another. For instance, let ‘fan speed’ and ‘temperature’ be attributes of two numerical data sets. A gradual item set “the higher the speed, the lower the temperature” (which correlates a data set’s attributes) becomes a GEP if it is less frequent (in terms of support as in frequent pattern mining) in one data set and more frequent in another. However, such patterns do not indicate how time gap impacts the emergence. Many correlations appear over time, for instance when phenomena appear after some meteorological situation due to latency. Previous works have not taken this temporal aspect into account. In this paper, we introduce temporal gradual emerging patterns (TGEPs) which are temporal gradual patterns (TGPs) whose frequency supports increase significantly between transformed data sets. For instance, a TGP “the higher the speed, the lower the temperature, almost 3 minutes later” becomes a TGEP if it occurs more frequently in one transformed data set than in another. Furthermore, we extend border manipulation to the case of mining TGEPs. In addition, we propose a more efficient ant colony optimization technique that exploits a heuristic approach to construct TGEPs.