  We prove the convergence of the spectrum of the generator of the kinetic
Brownian motion to the spectrum of the base Laplacian for closed Riemannian
manifolds. This generalizes recent work of Kolb--Weich--Wolf [arXiv:2011.06434]
on constant curvature surfaces and of Ren--Tao [arXiv:2208.13111] on locally
symmetric spaces. As an application, we prove a conjecture of Baudoin--Tardif
[arXiv:1604.06813] on the optimal convergence rate to the equilibrium.
