Several types of reinforced Nb 3Sn wires have been developed to prevent reduction of superconducting properties by applying a strong electromagnetic force. To fabricate a cryocooled magnet using those reinforced wires, we experimentally measured the minimum quench energy (MQE) under cryocooled conditions of some reinforced Nb 3Sn wires. As a result, it became clear that thermal stability expressed as MQE was controlled by the temperature margin between the temperature of the operating condition and the transition temperature from superconductivity to normal. Using the FEM analysis, it was realized that the cause of the decline in thermal stability for the reinforced wires was the low thermal conductivity of the reinforced materials.