The process of hydrogen desorption from graphane (graphene sheet saturated by hydrogen adsorbed from both sides) has been studied using the method of molecular dynamics. The temperature dependences of the time of desorption onset for various hydrogen coverages on graphene are calculated and the corresponding activation energies in the Arrhenius equation are determined. It is established that graphane exhibits a rather high thermal stability that makes possible its use in two-dimensional electronics even at room temperature. For the same reason, graphane can hardly be considered as a promising hydrogen storage material for fuel cells.