Infrared spectroscopy is the best astronomical tool for studying the composition of cosmic dust. Thanks to the Herschel satellite, dust properties from the FIR to mm wavelength range will be sampled in different astrophysical environments. In the laboratory, the study of the temperature and structural dependence of FIR absorption of cosmic dust analogs including agglomeration is essential to interpret observational spectra. For crystalline materials, FIR single phonon bands are temperature dependent due to the anharmonicity of the vibrational potentials. This strong temperature dependence of the FIR bands’ positions can be used as a thermometer of the dust temperature. In amorphous material, the FIR absorption is dominated by disorder-induced single phonon processes and in the submillimeter and millimeter range by highly temperature-dependent low energy processes, e.g. tunneling transitions in two-level systems. The effect of these processes on the FIR absorptivity in amorphous silicates will be demonstrated.