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