  We consider transport properties of disordered two-dimensional electron gases
under high perpendicular magnetic field, focusing in particular on the peak
longitudinal conductivity $\sigma_{xx}^\mathrm{peak}$ at the quantum Hall
plateau transition. We use a local conductivity model, valid at temperatures
high enough such that quantum tunneling is suppressed, taking into account the
random drift motion of the electrons in the disordered potential landscape and
inelastic processes provided by electron-phonon scattering. A diagrammatic
solution of this problem is proposed, which leads to a rich interplay of
conduction mechanisms, where classical percolation effects play a prominent
role. The scaling function for $\sigma_{xx}^\mathrm{peak}$ is derived in the
high temperature limit, which can be used to extract universal critical
exponents of classical percolation from experimental data.
