A theory for the existence of noninteracting small-scale, "drift" magnetic islands in a high temperature tokamak plasma is presented. This situation contrasts with that discussed by Rebut and Hugon [Plasma Phys. Controlled Fusion 33, 1085 (1991)] which involves a background "sea" of magnetic turbulence caused by island overlap. The islands are driven by the effect of finite ion Larmor radius on the particle drifts and they propagate with a velocity comparable to the diamagnetic velocity. In contrast with the work of Smolyakov [Plasma Phys. Controlled Fusion 35, 657 (1993)] collisions are assumed to be rare. Although the saturated island size is independent of the collision frequency in the model discussed here, collisions play a crucial role in determining the frequency of the magnetic islands. An estimate is made of the anomalous heat transport which results from the fluctuations in the electrostatic potential associated with these magnetic islands. The predicted thermal diffusivity has several, but not all, of the characteristies of the Rebut-Lallia-Watkins transport model.