In the apparatus for cooling a superconductor (1) in accordance with the present invention, a male thread portion (31) of an inner container (3) engages a female thread portion (21) of an outer container (2) so as to connect the inner and outer containers (2, 3) to each other. Also, the bottom wall of the inner container (3) is provided with a thermal conductor (6) penetrating therethrough. Further, a sapphire sheet (23) is joined to peripheral portions of an opening of the bottom wall of the outer container (2) facing the thermal conductor (6), so as to block the opening (26). As the distance between the bottom wall of the outer container (2) and the bottom wall of the inner container (3) is freely adjusted by changing the engaging position between the thread portions (21, 31), the gap between a high transition temperature (high-T c ) superconducting magnetic sensor (7) and the sapphire sheet (23) is adjusted.