We investigate correlated electronic transport in single-walled carbon nanotubes with two intramolecular tunneling barriers. We suggest that below a characteristic temperature the long-range nature of the Coulomb interaction becomes crucial to determine the temperature dependence of the maximum G(max) of the conductance peak. Correlated sequential tunneling dominates transport yielding the power law G(max) proportional to T(alphaend-end-1), typical for tunneling between the ends of two Luttinger liquids. Our predictions are in agreement with recent measurements.