The lithium intercalation into ion-beam sputter-deposited films of lithium manganese oxide is studied as a function of the film thickness (50–500nm). The kinetics of the intercalation is quantified in cyclic voltammetry under variation of the scanning rate over five orders of magnitude (0.005–768mV/s). With an increasing rate, the intercalation currents reveal a transition from a finite length diffusion to a semi-infinite diffusion behavior, as it is expected from continuum transport equations. But surprisingly, the peak current in the Randles-Sevcik regime scales with the square root of film thickness. Consequently, the diffusion coefficient apparently increases with the layer thickness. Combining the parameters of the actual microstructure of the thin films with an appropriate kinetic modeling that includes the effects of grain boundaries, it is shown that the observed acceleration is quantitatively understood by outstandingly fast short-circuit transport in a type B kinetic regime of grain boundary diffusion.