Superconducting magnetic energy storage (SMES) is more fast response, economical, and environment-friendly than uninterruptible power supply (UPS) using the battery. And the SMES not only has the ability to control active and reactive power simultaneously, but also has a long life time because the superconducting magnet does not have degradation problem which the battery has. Therefore, the SMES is a candidate for instead of the UPS using the battery. The SMES needs cryogenic system without exception. A conduction cooling system that has a simple, light and small structure is well adapted to high temperature superconducting (HTS) SMES. The cryogenic conduction cooling system is needed some technologies such as insulation, vacuum, and thermal analysis. Conduction heat is mainly transferred by cooler port, access port, support bar, etc., and radiation heat is transferred by vacuum chamber, thermal shield and HTS coil surface. The heat loads through the conduction and radiation of cryostat are calculated. Radiation shield heat load, temperature of HTS coil and conduction copper plate are estimated and measured. A cryopumping effect of cooled radiation shield was observed. A current lead and HTS coil heat load was evaluated to maintain HTS coil temperature was under 20 K.