Quantum transport including dephasing effects is of central fundamental topic in charge migration at the molecular scale. Especially the charge transport through organic semicondutors is dominated by activated hopping mechanism, thus it is important to understand the influence of the dephasing effects in detail for the development of molecular devices. Here we analyze the main role played by homogeneous dephasing effects onto the transport behaviour of 1D organic polymers systems using an extension of Büttiker's approach, which is the D'Amato-Pastawski model. With this model we analyze the transmission behavior as a function of the molecular length within both the coherent and incoherent regimes. We show that the charge transport mechanism of the systems displays a crossover from exponential decay (coherent) to Ohm's law (incoherent) as the length increases. We also dynamically study the transport response of molecular wires under the influence of thermal fluctuations. The transmission distributions obtained within dephasing regime demonstrate to be narrower than the coherent case since hopping mechanisms favor the charge transport even if the structure of the molecules are thermally perturbed. This work supports the interpretation of recent experiments obtained for long conjugated molecular wires.