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Organic multiferroic tunnel junctions (OMFTJs) with multi-resistance states have been proposed and drawn intensive interests due to their potential applications, for examples of memristor and spintronics based synapse devices. The ferroelectric control of spin-polarization at ferromagnet (FM)/ferroelectric organic (FE-Org) interface by electrically switching the ferroelectric polarization of the FE-Org has been recently realized. However, there is still a lack of understanding of the transport properties in OMFTJs, especially the interplay between the ferroelectric domain structure in the organic barrier and the spin-polarized electron tunneling through the barrier. Here, we report on a systematic study of the temperature dependent transport behavior in La0.6Sr0.4MnO3/PVDF/Co OMFTJs. It is found that the thermal fluctuation of the ferroelectric domains plays an important role on the transport properties. When T>120K, the opposite temperature dependence of resistance for in up and down ferroelectric polarization states results in a rapid diminishing of tunneling electroresistance (TER). These results contribute to the understanding of the transport properties for designing high performance OMFTJs for memristor and spintronics applications.