We propose a strategy to study the elastic properties of extremely thin graphene oxide (GO) films using Brillouin spectroscopy. The dependence of the surface acoustic wave of a gold capping layer on the structural, chemical and morphological changes occurring to the underneath GO film with temperature is reported and analyzed. At room temperature the shear constant c(44) is similar to 17 GPa and hardens up to 28 GPa at 100 degrees C due to the partial elimination of embedded water layers and to interlayer distance shrinking. At 200 degrees C the almost complete elimination of water induces layer stacking disorder, further GO-GO distance reduction and a significant increase of all elastic constants. The in-plane constants harden due to the partial restoration of the sp(2) C network (c(11): from 268 to 620 GPa) and the out of plane constants harden due to the H bonds that now directly connect the neighbouring GO layers (c(44) approximate to 80 GPa). The obtained Young's moduli are significantly higher than those reported for GO paper because the ultra-thin GO films are highly ordered and there is no macroscopic applied strain during the measurement. The results obtained here are associated with the intrinsic properties of GO as in-plane and inter-layer bonding.