In injection molding, cooling channels are usually manufactured with a straight shape, and thus have low cooling efficiency for a curved mold. Recently, additive manufacturing (AM) was used to fabricate conformal cooling channels that could maintain a consistent distance from the curved surface of the mold. Because this conformal cooling channel was designed to obtain a uniform temperature on the mold surface, it could not efficiently cool locally heated regions (hot spots). This study developed an adaptive conformal cooling method that supports localized-yet-uniform cooling for the heated region by employing micro-cellular cooling structures instead of the typical cooling channels. An injection molding simulation was conducted to predict the locally heated region, and a mold core was designed to include a triply periodic minimal surface (TPMS) structure near the heated region. Two biomimetic TPMS structures, Schwarz-diamond and gyroid structures, were designed and fabricated using a digital light processing (DLP)-type polymer AM process. Various design parameters of the TPMS structures, the TPMS shapes and base coordinates, were investigated in terms of the conformal cooling performance. The mold core with the best TPMS design was fabricated using a powder-bed fusion (PBF)-type metal AM process, and injection molding experiments were conducted using the additively manufactured mold core. The developed mold with TPMS cooling achieved a 15 s cooling time to satisfy the dimensional tolerance, which corresponds to a 40% reduction in comparison with that of the conventional cooling (25 s).