We study thermal phase slips in an infinite 2D superconducting film within the Usadel model. Recently, the free-energy instanton was obtained in the Ginzburg–Landau region in the vicinity of the critical current. The proximity to the critical current allows one to reduce the Ginzburg–Landau equations to the exactly integrable Boussinesq equation [1]. Using the scaling of the instanton parameters obtained in [1], we perform a gradient expansion of the Usadel equations near the critical current. Keeping only the leading terms in the free energy functional, we transform it into the Boussinesq form and find the activation barrier at arbitrary temperatures using the known instanton profile. In the 1D geometry, our approach yields the asymptotics of the barrier near the critical current, consistent with numerical results from [2]. [1] M. A. Skvortsov and A. V. Polkin, arXiv:2506.18130. [2] A. V. Semenov, P. A. Krutitskii and I. A. Devyatov, Jetp Lett. 92, 762 (2010)