Context. Many cosmic dust species, among them refractory oxides, form at temperatures higher than 300 K. Nevertheless, most astrophysical studies are based on the room-temperature optical constants of solids, such as corundum and spinel. A more realistic approach is needed for these materials, especially in the context of modeling late-type stars. Aims. We aimed at deriving sets of optical constants of selected, astrophysically relevant oxide dust species with high melting points. Methods. A high-temperature, high-pressure cell and a Fourier-transform spectrometer were used to measure reflectance spectra of polished samples. For corundum (α-Al 2 O 3 ), spinel (MgAl 2 O 4 ), and α-quartz (SiO 2 ), temperature-dependent optical constants were measured from 300 K up to more than 900 K. Small particle spectra were also calculated from these data. Results. All three examined oxides show a significant temperature dependence of their mid-IR bands. For the case of corundum, we find that the 13 μm emission feature -seen in the IR spectra of many AGB stars -can very well be assigned to this mineral species. The best fit of the feature is achieved with oblate corundum grains at (mean) temperatures around 550 K. Spinel remains a viable carrier of the 13 μ feature as well, but only for T < 300 K and nearly spherical grain shapes. Under such circumstances, spinel grains may also account for the 31.8 μm band that is frequently seen in sources of the 13 μm feature and which has not yet been identified with certainty.