Recent experimental and theoretical progress on semiconducting CaAgP prompted us to investigate in detail the electrical and thermal transport properties of this hexagonal pnictide, using first-principles calculations based on the density functional theory. In contrast to using a standard generalized gradient approximation, employing a hybrid Heyd-Scuseria-Ernzerhof functional yields its semiconducting nature, in agreement with the experimental observation with a bandgap of ∼0.15 eV. The narrow band gap semiconductor CaAgP, which under negative (chemical) pressure has been shown to turn into a nodal-line semimetal, is found to be dynamically stable, with a gapped electronic band structure when a hybrid functional is used. This is in an attractive range for applications in thermoelectric devices, and we have determined the lattice and electronic conductivity as a function of doping, which indeed predicts a promising thermoelectric performance, particularly for p-doped CaAgP.