Based on the Himawari-8 satellite TBB (Black Body Temperature) data from the Japan Meteorological Agency, the ERA5 (the fifth generation of European Centre for Medium-Range Weather Forecasts Reanalysis) reanalysis data from the European Centre for Medium-Range Weather Forecasts, and a new energy diagnostic method that uses a temporal scale for scale separation, the evolutionary characteristics of a convective cloud cluster from 0000 UTC 5 June to 1500 UTC 6 June 2016 (lasted 40 hours) that formed over the Tibetan Plateau (TP), moved eastward, and induced heavy precipitation in downstream regions were investigated in this study. The main findings are as follows. The main influencing systems for the eastward-moving convective cloud cluster at different stages of its lifespan were different. Before moving out of the plateau, the cloud cluster was mainly affected by a plateau vortex and a short-wave trough. As the cloud cluster vacated the plateau, the plateau vortex dissipated, whereas the short-wave trough intensified with time, and finally, the short-wave trough became the main influencing system of the cloud. The deep convection features of the eastward-moving cloud cluster were significant. The eastward-moving cloud cluster induced a series of precipitations from west to east, with the strongest precipitation occurring after the cluster had moved out of the plateau and its convective had lowered in height. The energetics characteristics of the eastward-moving convective cloud cluster experienced notable changes during the cluster lifespan, and the associated precipitation characteristics were also significantly different. When the cloud cluster was over the TP (the first stage), the contribution from the background field was a dominant factor. The background field provided energy for the evolution of eddy flow (by downscale kinetic energy cascade), which directly induced heavy precipitation. During the second stage, the precipitation-related latent heating was greatly enhanced, which significantly increased the APE (available potential energy) of eddy flow. Under the influences of vertical motion, the APE of eddy flow was released and converted to the KE (kinetic energy) of eddy flow. This acted as a dominant factor for the sustainment of the precipitation-related eddy flow. When the cloud cluster moved out of the TP, the influence of the background field on eddy flow was enhanced again; however, the influence was not direct as in the first stage. In this stage, the influence from the background environment favored the persistence of precipitation-related eddy flow indirectly. First, the APE of the background field was transferred to the APE of eddy flow through a downscale energy cascade. Then, a baroclinic energy conversion from the APE of the eddy flow to its KE occurred. This acted as a dominant energy source for the KE of eddy flow. Furthermore, in the third stage, a remarkable upscale energy cascade of KE was found, which reflected the feedback of eddy flow on its background field. However, the feedback intensity was not enough to significantly affect the evolution of the background field.