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This work explores the relation between magnetic islands, long range temporal correlations and heat transport. A low order rational surface (t = 3/2) was purposely scanned outward through an electron cyclotron resonance heated (ECRH) plasma in the TJ-II stellarator. Density turbulence and the poloidal flow velocity were characterized using a two channel Doppler reflectometer. Simultaneously, the ECRH power was modulated to characterize heat transport, using measurements from a 12 channel electron cyclotron emission diagnostic. A systematic variation of the poloidal velocity was found to be associated with the t = 3/2 rational surface. Near the rational surface, the Hurst exponent, quantifying the nature of long-range correlations, was reduced below 0.5 (indicating subdiffusion), while at radii smaller than that of the rational surface, it was found to be significantly enhanced (superdiffusion). In the latter region, heat transport was enhanced as well, thus establishing a link between density fluctuations and anomalous heat transport. The observed variation of the Hurst exponent was consistent with a magnetohydrodynamic turbulence simulation.