The goal of the present work was to study the bioleaching of chalcopyrite (CuFeS2), enargite (Cu3AsS4), and tennantite (Cu12As4S13) by pure and mixed cultures of moderately thermophilic microorganisms belonging to the groups predominant in technological processes (Acidithiobacillus caldus MBC-1, Sulfobacillus thermosulfidooxidans SH-1, and Acidiplasma sp. MBA-1) under different conditions (temperature of 40 to 60°C, presence of Fe2+ ions, pyrite (FeS2), and pyrrhotite (FeS)). Bioleaching of copper from chalcopyrite and enargite was shown to depend on temperature and to be almost independent of the composition of microbial culture. Under optimal conditions (50–55°C), after 30 days 25–27 and 14% of copper was leached from chalcopyrite and enargite, respectively. Increase in the temperature up to 60°C led to the inhibition of copper bioleaching from both minerals. The optimal temperature for tennantite bioleaching was 45°C, while the rate of bioleaching was significantly dependent on the composition of the microbial culture. In an experiment with a mixed culture of all three strains, 26% of copper was leached, while in experiments with pure cultures of A. caldus MBC-1, S. thermosulfidooxidans SH-1, and Acidiplasma sp. MBA-1, after 30 days 12, 21, and 18% of copper was leached, respectively. Addition to the medium of Fe2+ as ferrous sulfate resulted in an increased rate of copper leaching from enargite and tennantite, which may be explained by the fact that Fe3+ ions are generated during microbial Fe2+ biooxidation to Fe3+, which is a strong oxidizing agent and plays an important role in the leaching of sulfide minerals. In the presence of pyrite and pyrrhotite, the rates of enargite and tennantite leaching increased, probably due to the presence of Fe3+ ions in the medium, which were generated during the biooxidation of iron sulfide minerals. The results of the work demonstrated that different environmental factors affected the bioleaching of copper minerals in different ways, which is of practical importance, in particular, for planning the trials for bioleaching of mineral raw materials.