This paper presents a new approach to active sub-threshold leakage reduction using task migration. The main idea is to replicate a hot module in a design so as to actively migrate its computation at regular intervals, reducing the on-chip temperature and thereby the sub-threshold leakage. We observe that choosing which blocks to migrate and their placement in a floorplan is a chicken-and-egg problem. To solve this, we propose a two step floorplanning methodology, wherein, given a base floorplan, we first choose the modules to replicate and then effectively utilize the deadspaces in it by exploiting the lateral conduction of heat in the floorplan to place a module's replica. With an optimized floorplan, using task migration we obtain an average savings of 29% in the active sub-threshold leakage at the expense of about 6% additional area.