We report thermal expansion measurements on Ca(Fe1−xCox)2As2 single crystals with different thermal treatment, with samples chosen to represent four different ground states observed in this family. For all samples, thermal expansion is anisotropic with different signs of the in-plane and c-axis thermal expansion coefficients in the high temperature, tetragonal phase. The features in thermal expansion associated with the phase transitions are of opposite signs as well, pointing to a different response of transition temperatures to the in-plane and the c-axis stress. These features, and consequently the inferred pressure derivatives, are very large, clearly and substantially exceeding those in the Ba(Fe1−xCox)2As2 family. For all transitions the c-axis response is dominant.