Summary: $\alpha’$ corrections to near horizon dynamics of a Schwarzschild black hole in a large number of spacetime dimensions $D$ are governed by the worldsheet theory composed of the cigar CFT and the classical sigma model on the sphere at the horizon, along with a timelike-Liouville theory of central charge $26-D$. At leading order in weak string coupling, black hole thermodynamics is insensitive to the details of timelike Liouville theory. In this limit, we use target space replica-trick motivated infinitesimally off-shell closed string worldsheet formalism in  [arxiv: 2310.02313] to calculate thermal entropy exactly in $\alpha’$. The leading term in the $\alpha’\to 0$ limit and the first stingy correction of our result are in precise agreement with the target space Callan-Myers-Perry formula.