Transmission Mossbauer spectra at variable temperatures between 80 and 860 K have been collected for Co-substituted magnetities, CoxFe3-xO4, with x = 0.1, 0.2, and 0.4, and at two selected temperatures with the absorber in a longitudinal external magnetic field of 55 kOe. It is concluded that the interpretation of the spectra based on an earlier reported structural model leads to inconsistent results. An adequate and consistent description was obtained using a superposition of two model-independent hyperfine-field distributions, one arising from the tetrahedral (A) iron species, the second one from the octahedral (B) irons. The evaluated distributions clearly reveal the presence of two distinct B-site components, reflecting the existence of two different electronic states for the B-site irons at temperatures not exceeding almost-equal-to 650 K. The appearance of two B sites is quantitatively explained on the basis of structural considerations. At high temperatures, one of the B-site components gradually disappears in favor of the other, indicating that all B-site irons become involved in the electron-exchange process. The behavior of the A-site center shifts suggests that these sites become involved in the electron-exchange process at temperatures approaching or exceeding the Curie temperature. The A-site hyperfine field is adequately described by a Brillouin function. The obtained values for the A-A (10.5+/-1 K) and A-B (21.5+/-1.0 K) superexchange integrals give no indication as to whether they depend on the Co concentration. The nonlocalized-electron model is unable to reproduce the temperature dependence of the octahedral hyperfine field. Spectra at selected temperatures were obtained for compositions x = 0.6, 0.8, and 0.9. The A-site distributions are sharp and quite symmetric, whereas the shape of the B-site hyperfine-field distributions indicates the presence of more than two charge states for these iron species. For all considered compositions the magnetic order-disorder transition is sharp. The Curie temperature T(C) slightly decreases with increasing Co content. For x = 0.1, 0.2, and 0.4 the A-site electric-field gradient is close to zero, but not so for higher substitutions. The isomer shifts at a given temperature above T(C) decrease with increasing x, reflecting the evolution towards pure Fe3+ states.