Controlling the thermal energy of lattice vibrations separately from electrons is vital to many applications including electronic devices and thermoelectric energy conversion. To remove heat without shorting electrical connections, heat must be carried in the lattice of electrical insulators. Phonons are limited to the speed of sound, which, compared to the speed of electronic processes, puts a fundamental constraint on thermal management. Here we report a supersonic channel for the propagation of lattice energy in the technologically promising piezoelectric mineral fresnoite (Ba2TiSi2O8) using neutron scattering. Lattice energy propagates 2.8−4.3 times the speed of sound in the form of phasons, which are caused by an incommensurate modulation in the flexible framework structure of fresnoite. The phasons enhance the thermal conductivity by 20% at room temperature and carry lattice-energy signals at speeds beyond the limits of phonons.