The self-diffusion of a lamellae-forming nonentangled PEP-PDMS diblock copolymer was investigated with pulsed Geld gradient (PFG) NMR,in dependence on temperature. The order-to-disorder transition (ODT), which occurs at T = 64 degrees C, was traversed. Coming from the disordered state, a sudden increase of the width of the distribution of self-diffusivities was observed (an increase of the nonexponentiality of the echo attenuation) when crossing the ODT. This is caused by the onset of anisotropic diffusion along the lamellae whose orientations are isotropically distributed. The weakness of the nonexponentiality leads to the conclusion that the range of local order in the grains is much smaller than the grain size (determined by small-angle light scattering). In addition, the temperature dependence of the self-diffusivity shows a substantial slowing down, when approaching the ODT from the disordered state which is attributed to the effect of concentration fluctuations. The self-diffusion measurements are compared with earlier measurements of the zero shear viscosity and dynamic light scattering on this polymer and with Monte Carlo simulations from the Literature. The results from all of these methods are consistent.