As the melt front gradually moves away from the heat source during the heat transfer process, phase change materials (PCMs) inevitably cause the heat transfer efficiency to decrease with heat transfer time, especially for a shaped PCM (SPCM). In this study, it is proposed to compress the SPCM phase-changed region by pressure to reduce the thermal resistance between the heat source and the phase transition interface, thus slowing down the rate of heat transfer efficiency decrease. We established a one-dimensional semi-infinite compression heat transfer theoretical model and prepared a thermoelastic SPCM (TESPCM) for compression heat transfer experiments, which verified the reliability of the theoretical model. Experimental demonstrate that the pressure enhancement contributes to the heat transfer efficiency and becomes more pronounced with heat transfer time. The pressure-enhanced heat transfer was analyzed by the theoretical model with the following conclusions: pressure enhancement not only improves the latent heat utilization, heat transfer cut-off time, and maximum tolerable heat flux of TESPCM but also increases the specific energy and specific power of TESPCM. The effect of pressure on heat transfer efficiency tends to accelerate with increasing compression. Furthermore, the improvement of heat transfer by pressure enhancement becomes more significant with the increase of thermal conductivity, but the effect of latent heat on temperature control decreases with the increase of compression.