Stimuli-responsive/smart drug delivery systems (DDSs), particularly those that use temperature as a stimuli-response factor to activate drug release, are the subject of recent research. A phase change material (PCM) is a popular thermally responsive material that can be used as a drug carrier and only when the system temperature is above the phase change point is the drug released following the phase change material changing from solid to liquid. In this study, a novel NIR light-triggered temperature-sensitive drug delivery system is developed for controllable release of acyclovir (ACV). For this purpose, a mixture of a phase change material (T38) and an ACV compound is first emulsified with copper oxide nanoparticles (CuO NPs) as a Pickering stabilizer and a photothermal conversion material, and then encapsulated with SiO2 to form a photothermal stimuli-responsive delivery system. This system shows a uniform spherical shape with a well-distinct core-shell structure, and is further experimentally proven to be able to controllably release drugs with solid-liquid transition of the phase change carrier upon temperature change. These results indicate that cumulative release of ACV can reach 51.2% at 40 °C within 20 hours, which is much higher than 27.3% release achieved below the melting point of T38. In addition, CuO NPs with excellent photothermal conversion ability endow the system with precisely controllable drug delivery via NIR light stimulation, where the cumulative drug release can reach 83.6% after 7 cycles of light stimulation, allowing controlled release at a specific time or location.