A large amount of research has been invested in the last years to investigate electron transfer and transport in DNA molecules. Partially contradicting results have been obtained; so was DNA identified as insulator, wide-band gap semiconductor or metallic. Several factors like base-pairs sequences, static and dynamic disorder and properties of the environment have been shown to strongly influence charge propagation along the double helix. We focus on environmental effects and investigate within a model Hamiltonian approach electronic transport in a DNA-like wire strongly coupled to a dissipative bath, which mimics the effect of counterions and hydration shells. We find a bath-induced pseudo-gap in the electronic structure of the wire, which leads to a crossover from a purely semiconducting behavior with a "true" gap (zero density of states) in the electronic transmission to a metallic behaviour induced by thermal bath fluctuations. As a result the temperature dependence of the transmission near the Fermi energy manifests activated Arrhenius-like behavior and it shows a weakly exponential dependence on the wire length, indicative of strong incoherent transport.