The prefactor of the activated dissipative conductivity in a plateau range of the quantum Hall effect is studied in the case of a long-range random potential. It is shown that due to the long time it takes for an electron to drift along the perimeter of a large percolation cluster, phonons are able to maintain quasiequilibrium inside the cluster. The saddle points separating such clusters may then be viewed as ballistic point contacts between electron reservoirs with different electrochemical potentials. The network of ballistic conductances is shown to determine the conductivity. The prefactor is universal and equal to 2e2h at an integer filling factor.