The thermodynamic parameters that drive the atomic migration in B2 alloys are studied using Monte-Carlo simulations. The model is based on a vacancy jump mechanism between nearest neighbor sites, with a constant vacancy concentration. The ordering energy is described through an Ising Hamiltonian with interaction potentials between first and second nearest neighbors. Different migration barriers are introduced fur A and B atoms. The results of the simulations compare very well with those of experiments. The ordering kinetics are well described by exponential-like behaviors with two relaxation times whose temperature dependences are Arrhenius laws yielding effective migration energies. The ordering energy contributes significantly to the total migration energy.