We calculate the linear response conductance of electrons in a Luttinger liquid with arbitrary interaction g_{2}, and subject to a potential barrier of arbitrary strength, as a function of temperature and/or the length of interaction region. Our result agrees with known limiting cases. We first map the Hamiltonian in the basis of scattering states into an effective low energy Hamiltonian in current algebra form. Analyzing the perturbation theory in the fermionic representation the diagrams contributing to the renormalization group (RG) beta-function are identified. The universal part of beta-function is given by a ladder series and is summed to all orders in g_{2}. The RG-equation for temperature dependent conductance is solved analytically. A non-universal part of beta-function beyond the ladder series is discussed and compared to the recent exact solution of the problem.