In the frame of the planned luminosity upgrade of the Large Hadron Collider, new quadrupole and dipole magnets are being designed and tested. Cabled conductors have been tested in the FRESCA test station to aid this effort. Part of this work is to characterize the thermal stability of the Nb3Sn conductors, because this is difficult to measure in a real magnet. When measured at nominal operating current at 1.9 and 4.3 K, the minimum quench energy (MQE) diminishes when the system is cooled. When the temperature is decreased but the nominal current is increased to profit from the increased Ic, the temperature margin across the entire magnet cross-section decreases. Unlike Nb-Ti, Nb3Sn conductors are not aided by the super-fluidity of the helium in the magnet because they are impregnated. It is argued here that given the material properties and effects, the MQE decreases with decreasing temperature. This conclusion is validated experimentally and is used to determine the MQE in a Large Hadron Collider quadrupole upgrade magnet.