The thermal conductivity of marble, gabbro, quartz-monzonite, basalt and of labradorite was measured between 0.3 and 80 K. In all cases, the phonon mean free paths l¿ were found to increase with decreasing temperature, but even at the lowest temperatures, l¿ was far smaller than the average grain sizes. This demonstrates that phonon scattering by grain boundaries has very little influence on the heat transport in these rocks. Evidence is presented that lamellae due to twinning or exsolution, rod-like large inclusions, and density fluctuations inside the grains mask the effect of grain boundaries.