The minimum quench energy ( ) and normal zone propagation velocity ( ) of three kinds of Nb 3 Al superconductors fabricated by the rapid heating, quenching and transformation (RHQT) process were measured under various conditions of applied magnetic field (10-14 T), temperature (7-11 K), and transport current (80-95% of the critical current), while cooled by a cryocooler for developing the over 20-T class cryogen-free magnet. As a result, values were related to the critical current density ( c ); high MQE was obtained for low c . It is assumed that c has a stronger influence on the than specific heat, thermal conductivity, resistivity, and other parameters of the composite superconductor including the matrix and the stabilizer.was mainly proportional to the transport current density varying with applied field and temperature. The second contribution to is assumed to be heat capacity depending on the wire configuration.