  We develop a temperature dependent theory for singlet exciton hopping
transport in disordered semiconductors. It draws on the transport level concept
within a F\"orster transfer model and bridges the gap in describing the
transition from equilibrium to non-equilibrium time dependent spectral
diffusion. We test the validity range of the developed model using kinetic
Monte Carlo simulations and find agreement over a broad range of temperatures.
It reproduces the scaling of the diffusion length and spectral shift with the
dimensionless disorder parameter and describes in a unified manner the
transition from equilibrium to non-equilibrium transport regime. We find that
the diffusion length in the non-equilibrium regime does not scale with the the
third power of the F\"orster radius. The developed theory provides a powerful
tool for interpreting time-resolved and steady state spectroscopy experiments
in a variety of disordered materials, including organic semiconductors and
colloidal quantum dots.
