Picosecond time-resolved far-infrared measurements are presented of the scattering between conduction-band states in a doped quasi quantum dot. These states are created by the application of a magnetic field along the growth direction of an InAs/AlSb quantum well. A clear suppression of the cooling rate is seen, from 10¹² s^-1 when the level spacing is equal to the phonon energy, to 10¹⁰ s^-1 away from this resonance, and thus the results provide unambiguous evidence for the phonon bottleneck. Furthermore, the lifetimes had only weak dependence on temperature between 4 and 80 K.