The generalized Heusler compounds Mn(2)CoZ (Z = Al, Ga, In, Si, Ge, Sn, Sb) with the Hg(2)CuTi structure are of great interest due to their half-metallic ferrimagnetism. The complex magnetic interactions between the constituents are studied by means of first principles calculations of the Heisenberg exchange coupling parameters, and Curie temperatures are calculated from those. Due to the direct Mn-Mn exchange interaction in Mn(2)CoZ, the Curie temperature decreases, although the total moment increases when the valence electron number Z is increased. The exchange interactions are dominated by a strong direct exchange between Co and its nearest neighbor Mn on the B site, which is nearly constant. The coupling between the nearest neighbor Mn atoms scales with the magnetic moment of the Mn atom on the C site. Calculations with different lattice parameters suggest a negative pressure dependence of the Curie temperature, which follows from the decreasing magnetic moments. Curie temperatures of more than 800 K are predicted for Mn(2)CoAl (890 K), Mn(2)CoGa (886 K), and Mn(2)CoIn (845 K).