A- and B-site ordered quadruple perovskites with the chemical formula AA3′B2B2′O12 can form with 1:3 ratio at the A site. A unique feature of this specially ordered perovskite is that three different atomic sites (A′, B, and B′ sites) can all accommodate magnetic transition metals. As a consequence, multiple magnetic and electronic interactions can occur at A′, B, and/or B′ sites, giving rise to a series of intriguing physical phenomena. CaCu3Fe2Re2O12 is a good example, which shows half-metallic electronic structure, large magnetization, and a very high Curie temperature. Here we investigated a series of ferrimagnetic (FiM) compounds ACu3Fe2Re2O12 (A=Ca, Sr, Ba, Pb, Sc, Y, La) by using density functional theory and Monte Carlo simulations. We found that all compounds with A2+ ions exhibit high Curie temperatures (above 405 K), and the compounds with A3+ substitution yield even higher TC (above 502 K). By examining interatomic exchange parameters, we found that the antiferromagnetic exchange couplings between Re and Cu as well as Re and Fe are responsible for this very high Curie temperature. For the compounds with A3+ substitution, electron doping in bands around the Fermi level dominated by the Re ions strengthens the Re-Cu, Re-Fe, and Re-Re exchange interactions, which cause an increase in the critical temperature. Finally, we calculated the formation energies of the quadruple perovskites with respect to the possible decomposition pathways and have found that the values are reasonable for the synthesis of these compounds under the conditions of high pressure and high temperature. In summary, this work demonstrates a design strategy of enhancing the spin ordering temperature by replacing A-site nonmagnetic ions.