  We conduct an analysis of the quasi-normal modes for generic spin
perturbations of the Kerr black hole using the isomonodromic method. The
strategy consists of solving the Riemann-Hilbert map relating the accessory
parameters of the differential equations involved to monodromy properties of
the solutions, using the $\tau$-function for the Painlev\'e V transcendent. We
show good accordance of the method with the literature for generic rotation
parameter $a<M$. In the extremal limit, we determined the dependence of the
modes with the black hole temperature and establish that the extremal values of
the modes are obtainable from the Painlev\'e V and III transcendents.
