Extending TMD factorization to thrust-dependent observables entails difficulties ultimately associated with the behavior of soft radiation. As a consequence, the definition of the TMDs has to be revised, while keeping (and extending) its universality properties. Moreover, the regularization of the rapidity divergences intertwines with the thrust dependence, leading to a new kind of factorization theorem, with unexpected features. In this talk, I will show how to properly factorize the thrust distribution of $e^+e^-$ annihilation into a single hadron, whose transverse momentum is measured with respect to the thrust axis. The cross section is presented up to NNLL-accuracy in thrust and compared with BELLE data.