  The "textbook" phonon mean free path (MFP) of heat carrying phonons in
silicon at room temperature is ~40 nm. However, a large contribution to the
thermal conductivity comes from low-frequency phonons with much longer MFPs. We
present a simple experiment demonstrating that room temperature thermal
transport in Si significantly deviates from the diffusion model already at
micron distances. Absorption of crossed laser pulses in a freestanding silicon
membrane sets up a sinusoidal temperature profile that is monitored via
diffraction of a probe laser beam. By changing the period of the thermal
grating we vary the heat transport distance within the range ~1-10 {\mu}m. At
small distances, we observe a reduction in the effective thermal conductivity
indicating a transition from the diffusive to the ballistic transport regime
for the low-frequency part of the phonon spectrum.
