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A quadratic optimal transport metric on the set of probability measure over$\R^2$ is introduced. The quadratic cost is given by the euclidean norm on$\R^2$ associated to some well chosen symmetric positive matrix, which makesthe metric equivalent to the usual Wasserstein-2 metric. The dissipation of thedistance to the equilibrium along the kinetic Fokker-Planck flow, is bounded bybelow in terms of the distance itself. It enables to obtain some new type oftrend to equilibrium estimate in Wasserstein-2 like metric, in the case ofnon-convex confinement potential.

An optimal transport approach of hypocoercivity for the 1d kinetic Fokker-Plank equation