Deep-sea corals are a potentially valuable archive of the temperature and ocean chemistry of intermediate and deep waters. Living in near-constant temperature, salinity, and pH and having amongst the slowest calcification rates observed in carbonate-precipitating biological organisms, deep-sea corals can provide valuable constraints on processes driving mineral equilibrium and disequilibrium isotope signatures. Here we report new data to further develop "clumped" isotopes as a paleothermometer in deep-sea corals as well as to investigate mineral-specific, taxon-specific, and growth-rate-related effects. Carbonate clumped isotope thermometry is based on measurements of the abundance of the doubly substituted isotopologue (COO2)-C-13-O-18-O-16 in carbonate minerals, analyzed in CO2 gas liberated on phosphoric acid digestion of carbonates and reported as Delta(47) values. We analyzed Delta(47) in live-collected aragonitic scleractinian (Enallopsammia sp.) and high-Mg calcitic gorgonian (Isididae and Coralliidae) deep-sea corals and compared results to published data for other aragonitic scleractinian taxa. Measured Delta(47) values were compared to in situ temperatures, and the relationship between Delta(47) and temperature was determined for each group to investigate taxon-specific effects. We find that aragonitic scleractinian deep-sea corals exhibit higher values than high-Mg calcitic gorgonian corals and the two groups of coral produce statistically different relationships between Delta(47)-temperature calibrations. These data are significant in the interpretation of all carbonate clumped isotope calibration data as they show that distinct Delta(47)-temperature calibrations can be observed in different materials recovered from the same environment and analyzed using the same instrumentation, phosphoric acid composition, digestion temperature and technique, CO2 gas purification apparatus, and data handling. There are three possible explanations for the origin of these different calibrations. The offset between the corals of different mineralogy is in the same direction as published theoretical predictions for the offset between calcite and aragonite although the magnitude of the offset is different. One possibility is that the deep-sea coral results reflect high-Mg and aragonite crystals attaining nominal mineral equilibrium clumped isotope signatures due to conditions of extremely slow growth. In that case, a possible explanation for the attainment of disequilibrium bulk isotope signatures and equilibrium clumped isotope signatures by deep-sea corals is that extraordinarily slow growth rates can promote the occurrence of isotopic reordering in the interfacial region of growing crystals. We also cannot rule out a component of a biological "vital effect" influencing clumped isotope signatures in one or both orders of coral. Based on published experimental data and theoretical calculations, these biological vital effects could arise from kinetic isotope effects due to the source of carbon used for calcification, temperature-and pH-dependent rates of CO2 hydration and/or hydroxylation, calcifying fluid pH, the activity of carbonic anhydrase, the residence time of dissolved inorganic carbon in the calcifying fluid, and calcification rate. A third possible explanation is the occurrence of variable acid digestion fractionation factors. Although a recent study has suggested that dolomite, calcite, and aragonite may have similar clumped isotope acid digestion fractionation factors, the influence of acid digestion kinetics on Delta(47) is a subject that warrants further investigation.