In coils using low temperature superconductor, a wire motion due to an electromagnetic force observably reduces stability. It is quite important to prevent the wire motion under a DC operation. We aim to improve stability by means of an intensification of a winding tension at cryogenic temperature. The technique is the use of the bobbins whose thermal expansion coefficients are negative. For experiments, superconducting coils were fabricated with various conditions; materials of bobbins, thermal expansion properties, and winding tensions at room temperature. And quench characteristics were measured under the DC operation. Applying a standard deviation of quench currents, we discussed about the relation between fluctuation and the amplitude of the quench currents. In the results, stable quench characteristics were obtained in the coils which were not extremely contracted in the direction of the circumference.