In recent years, the quality of high-temperature superconductors (HTS) has been improving. Our goal is to apply an HTS coil to superconducting magnetic energy storage, because an HTS coil is more thermally stable than a low-temperature superconductor coil owing to high thermal margin during its transition to the normal state and its high thermal capacity at a high operational temperature. On the other hand, to enhance the reliability and safety of an HTS coil, it is necessary to establish a stability criterion to prevent thermal and mechanical damages during a quench. Therefore, we have to clarify the thermal behavior of a cryocooler-cooled HTS coil assuming practical applications. In this study, we evaluated the cooling effect using a numerical simulation and thermal conduction experiments. The numerical simulation was based on the finite element analysis, and the thermal conduction experiments were carried out on a model coil wound with electrically insulated copper and stainless steel laminated tapes. These had the same shape and dimensions as YBCO tape, assuming an application to an superconducting magnetic energy storage coil. We focused especially on the cooling effect of a winding with paraffin impregnation compared with that of a dry winding.