Motivated by recent inelastic neutron scattering experiments we examine the magnetic properties of LiV2O4. We consider a model which describes the half-filled localized A1g spins interacting via frustrated antiferromagnetic Heisenberg exchange and coupled by local Hund's interactions with the 1/8-filled itinerant Eg band and study it within an exact diagonalization scheme. In the present study we limited the analysis to the case of the cluster of two isolated tetrahedrons. We found that both the ground state structure and low-lying excitations depend strongly on the value of Hund's coupling, which favours the triplet states. With increasing temperature the triplet states become more and more populated, which results in the formation of non-zero residual magnetic moment. We present the temperature dependence of the calculated magnetic moment and of the spin-spin correlation functions at different values of Hund's coupling and compare them with the experimental results.