This work explores the relation between magnetic islands, long range temporal correlations and heat transport. A low order rational surface (ῑ = 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 (or radial electric field) 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 stationaryῑ = 3/2 magnetic island. Inside from the rational surface, the Hurst coefficient, quantifying the nature of long-range correlations, was found to be significantly enhanced. Simultaneously, heat transport was enhanced as well, establishing a clear link between density fluctuations and anomalous heat transport. The variation of the Hurst coefficient was consistent with a magnetohydrodynamic turbulence simulation.