We derive high- temperature series expansions for the spin correlation functions of the A-spinel lattice. The development is extended to the order 6 in β = 1/_KBT with nearest-neighbour and next-nearest neighbour interactions. The results are given for various neighbour correlation functions (up to the third). The behaviour with the temperature is presented. The critical region is studied by applying the Padé approximants method to the corresponding high- temperature series expansion of the magnetic susceptibility and the correlation length. The approach is applied to the experimental results of the particular system A-spinel CoCo₂O₄ . The following estimates are obtained for the familiar critical exponents:  γ =  1.382±0.010 and ν =  0.701±0.012.