In this paper, we propose algorithms to minimize the energy consumption in millimeter wave/terahertz multi-user downlink communication systems. To ensure coverage in blockage-vulnerable high frequency systems, we consider cooperative rate-splitting (CRS) and transmission over multiple time blocks, where via CRS, multiple users cooperate to assist a blocked user. Moreover, we show that transmission over multiple time blocks provides benefits through smart resource allocation. We first propose a communication framework named improved distinct extraction-based CRS (iDeCRS) that utilizes the benefits of rate-splitting. With our transmission framework, we derive a performance benchmark assuming genie channel state information (CSI), i.e., the channels of the present and future time blocks are known, denoted as GENIE. Using the results from GENIE, we derive a novel efficiency constrained optimization (ECO) algorithm assuming instantaneous CSI. In addition, a simple but effective even data transmission (EDT) algorithm that promotes steady transmission along the time blocks is proposed. Simulation results show that ECO and EDT have satisfactory performances compared to GENIE. The results also show that ECO outperforms EDT when many users are cooperating, and vise versa.