The transient inter-valence-band absorption in p-type germanium investigated with picosecond excitation and probe pulses in the mid-infrared gives direct information on the time evolution of hot-hole distributions. Spectrally and temporally resolved measurements are reported for different carrier concentrations between ${10}^{16}$ and ${10}^{17}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ and for lattice temperatures from 30 to 300 K. A fast bleaching of the heavy-hole-to-light-hole transition is followed by an absorption increase after excitation at wavelengths around 10 \ensuremath{\mu}m. The strength and the picosecond decay times of the two contributions depend on the initial carrier temperature, the pumping intensity, and the spectral position of the probe pulses. Subpicosecond carrier-carrier and inter-valence-band scattering lead to the rapid formation of an equilibrium distribution of hot heavy holes which cools predominantly by emission of optical phonons on a time scale of several tens of picoseconds. Theoretical simulations of carrier cooling give a coupling constant of the optical deformation potential of ${\mathit{D}}_{0}$=6.3\ifmmode\times\else\texttimes\fi{}${10}^{8}$ eV/cm.