We have measured the temperature dependence of the conductance of long V-groove quantum wires fabricated using GaAs/AlGaAs heterostructures, in a wide temperature range (200 mK < T < 4.2 K). We find that for our quantum wires the Fermi velocity can be as low as nu(F) congruent to 5 x 10(4) m/s, corresponding to an interaction parameter value of g congruent to 0.56. This value suggests that our data are consistent with theories developed within the framework of the Luttinger liquid model in the presence of a single strong barrier (weak link).