We investigate the effective transport of a sorptive solute through a chemically heterogeneous medium subject to temporal fluctuations of the flow conditions. We focus on linear instantaneous sorption, with a spatially variable retardation factor. The medium is physically homogeneous. The temporal variability of the flow is represented by a stationary random process. In this stochastic modelling framework, solute spreading is quantified by effective dispersion coefficients. Focusing on the transverse contributions due to chemical heterogeneity and temporal fluctuations, we find enhanced transverse spreading characterized by a transverse effective dispersion coefficient that, in contrast to transport in steady state flow, evolves to a disorder-induced macroscopic value independent of local dispersion.

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