The layered misfit cobaltate CaCoO, also known as CaCoO[CoO], is a promising p-type thermoelectric oxide. Employing density functional theory, we study its electronic structure and determine, on the basis of Boltzmann theory within the constant-relaxation-time approximation, the thermoelectric transport coefficients. The dependence on strain and temperature is determined. In particular, we find that the XX-component of the thermopower is strongly enhanced, while the yy-component is strongly reduced, when applying 2% tensile strain. A similar anisotropy is also found in the power factor. The temperature dependence of the conductivity in the a-b plane is found to be rather weak above 200 K, which clearly indicates that the experimentally observed transport properties are dominated by inhomogeneities arising during sample growth, i.e., they are not intrinsic.