The temperature gives one an idea of the level of the optically thick layer of water vapor. A warmer temperature means that the water vapor is lower than a neighboring cooler region at a fixed time. Compare the region about 20N and 140W in both figures. One can see that in time the region warmed significantly. Since the region of dark red in Figure 1 had expanded in time, this implies that sinking motion was responsible for the warming.
Time changes in temperautre can imply vertical motion in the Lagrangian frame.
If there is no temperature change then there is no vertical motion in this frame of reference.