Recently, the issue of energy consumption of the UEs in heterogeneous networks has rapidly become a research focus area of the entire telecommunications community. This issue is obviously critical because the energy consumption of UEs can severely degrade their already limited battery capacity. In this article, we consider a heterogeneous network environment comprising base stations (each of which is also referred to as an eNB) with embedded storage that can serve as an effective cache-based traffic offloading technology in scenarios where many UEs simultaneously want to access popular contents of sports matches, live music events, and so forth. However, if many UEs are connected to only a few eNBs, they suffer from degraded throughput and increased transmission time. This longer transmission time eventually leads to increased energy consumption of UEs. To deal with this challenge, we propose an algorithm to reassign UEs to eNBs to minimize the total energy consumption of UEs with the constraint that their throughput is guaranteed. The effectiveness of our proposed algorithm is evaluated through computer-based simulations.