The minimum quench energies (MQEs) of superconducting (SC) wires have been measured precisely by means of a 'Carbon Paste Heater'. The thermal behavior just before the normal generation of the heavy loaded SC wire was observed to determine the quenching. We learned that once a normal region is produced, it should spread rapidly regardless of the surrounding conditions. The MQE, however, would increase when a local temperature rise before quenching is prevented by using certain materials around the SC wire. For example, high thermal diffusivity in impregnating materials or low thermal conductivity in wire insulation will be needed when disturbances occur outside of the SC wires. In the previous paper, we showed the effects of enamel insulation for improving stability. Thus, in this study, we examine the relation between MQE and the thermal properties of the impregnating material. Several kinds of impregnating materials were selected and the thermal properties are compared with enlarging MQE in mind. We have searched for an impregnating material that has the thermal property required for improved stability.