We present an ab initio study of MgO at high temperature and pressure, around the phase transition between the B1 and B2 phases. By means of ab initio molecular dynamic calculations, the thermal evolution of vibrational properties and thermodynamic quantities are obtained. We carefully compare our results with previous theoretical works on the phase transition curve and we analyse the differences among them. We show that anharmonic effects have been underestimated in the quasiharmonic approximation and that their inclusion in the free energy strongly straighten up the transition curve. Then we use our B1-B2 phase boundary and our calculated Hugoniot to analyze recent decaying shock experiments on MgO. We also provide important thermodynamic quantities as the Grüneisen parameter and sound velocities and we discussed their temperature dependence.