We present a theoretical investigation of the tracer diffusion of diblock copolymers and homopolymers in a thermally fluctuating block copolymer melt above the order-disorder transition (ODT) temperature. Entanglement effects and differences in monomeric friction coefficients are ignored; hence, the theory should be most applicable to short copolymers with theologically similar blocks. Overall, we find that the diffusion rates of both tracer block copolymers and homopolymers in a block copolymer melt are suppressed when compared with diffusivities in a strictly homogeneous medium with the same average composition. This mobility suppression is due to thermally excited composition fluctuations in block copolymer melts near the ODT; the latter result in transient potential barriers to diffusion. We explore the dependence of the tracer diffusion coefficient on molecular weights and compositions of both matrix and tracer, as well as temperature. A comparison of our theoretical predictions to recent experiments by T. Lodge and coworkers shows qualitative agreement.