Carbonates have repeatedly been discussed as possible carriers of stardust emission bands. However, the band assignments proposed so far were mainly based on room-temperature powder transmission spectra of the respective minerals. Since very cold calcite grains have been claimed to be present in protostars and in planetary nebulae (PNs) such as NGC 6302, the changes of their dielectric functions at low temperatures are relevant from an astronomical point of view. We have derived the infrared optical constants of calcite and dolomite from reflectance spectra, measured at 300, 200, 100, and 10 K, and calculated small-particle spectra for different grain shapes, with the following results. (1) The absorption efficiency factors of both calcite and dolomite are extremely dependent on the particle shapes. This is due to the high peak values of the optical constants of CaCO 3 and CaMg[CO 3 ] 2 . (2) The far-infrared properties of calcite and dolomite also depend very significantly on the temperature. Below 200 K, a pronounced sharpening and increase in the band strengths of the far-infrared resonances occurs. (3) In view of the intrinsic strength and sharpening of the $44 m band of calcite at 200-100 K, the absence of this band, inferred from Infrared Space Observatory data, in PNs requires dust temperatures below 45 K. (4) Calcite grains at such low temperatures can account for the ''92'' m band, while our data rule out dolomite as the carrier of the 60-65 m band. The optical constants presented here are publicly available in the AIU Jena Database of Optical Constants for Cosmic Dust.