The effects of a partial replacement of Ordinary Portland cement (OPC) with three types of calcium sulfoaluminate (CSA) cements (40 wt% and 20 wt%) were investigated. The obtained results were generally in agreement with previously published data but with few interesting exceptions. Setting times were shortened due to the formation of ettringite. The maximum hydration temperature increased for concretes containing 40 wt% of CSA but decreased when 20 wt% replacement was used. The decrease was related to the deficiency of the available sulfates, which limited the formation of ettringite. The presence of extra anhydrite and calcium oxide was associated to the delayed establishment of the second temperature peak in contrast to OPC-based concretes. Their surplus delayed calcium aluminate and belite reactions, and triggered renewed formation of ettringite, C-S-H and portlandite. Effects of aluminum hydroxide were also indicated as possibly important, although not proved experimentally in this research. The slightly lower compressive strength measured for mixes containing 40 wt% of CSA were linked with more formed ettringite. The same factor was indicated as the key to the reduction of the total shrinkage in mixes containing 40 wt% of CSA and increased for the lower CSA replacement level. In that case, the insufficient amount of formed ettringite caused too small expansion, which could not efficiently mitigate or compensate the developed shrinkage.