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Relaxation of soft modes (e.g. charge density in gated semiconductorheterostructures, spin density in the presence of magnetic field) slowed downby disorder may lead to giant enhancement of energy transfer (cooling power)between overheated electrons and phonons at low bath temperature. We show thatin strongly disordered systems with time-reversal symmetry broken by externalor intrinsic exchange magnetic field the cooling power can be greatly enhanced.The enhancement factor as large as $10^{2}$ at magnetic field $B \sim 10$ Teslain 2D {\rm InSb} films is predicted. A similar enhancement is found for theultrasound attenuation.

Magnetic field-induced giant enhancement of electron-phonon energy transfer in strongly disordered conductors