  We use a general diagrammatic formalism based on a local conductivity
approach to compute electronic transport in continuous media with long-range
disorder, in the absence of quantum interference effects. The method allows us
then to investigate the interplay of dissipative processes and random drifting
of electronic trajectories in the high-temperature regime of quantum Hall
transitions. We obtain that the longitudinal conductance \sigma_{xx} scales
with an exponent {\kappa}=0.767\pm0.002 in agreement with the value
{\kappa}=10/13 conjectured from analogies to classical percolation. We also
derive a microscopic expression for the temperature-dependent peak value of
\sigma_{xx}, useful to extract {\kappa} from experiments.
