The specific heat C(p) and the thermal conductivity lambda of a series of base-catalyzed silica aerogels have been measured at temperatures between 0.05 and 20 K. The results confirm that the different length-scale regions observed in the aerogel structure are reflected in the dynamic behavior of these materials. The analysis of the C(p) and lambda-data reveals three different temperature regimes where the contributions of phonon, fracton, and particle modes can be separated and identified. In particular, we discuss the crossover behavior linking the phonon and the fracton regime and we consider the possibility of two spectral dimensions characterizing the fracton modes. Our data imply important differences between the physical mechanisms dominating the low-temperature behavior of aerogels and dense glasses, respectively. From our analysis we also conclude that the low-temperature properties of amorphous SiO2 are most likely not due to fractal behavior.