We present a scheme to measure the displacement of a nanomechanical resonator at cryogenic temperature. The technique is based on the use of a superconducting quantum interference device to detect the magnetic flux change induced by a magnetized particle attached on the end of the resonator. Unlike conventional interferometric techniques, our detection scheme does not involve direct power dissipation in the resonator, and therefore, is particularly suitable for ultralow temperature applications. We demonstrate its potential by cooling an ultrasoft silicon cantilever to a noise temperature of 25 mK, corresponding to a subattonewton thermal force noise of 0.5 aN/.