  Using generalized hydrodynamics (GHD), we exactly evaluate the
finite-temperature spin Drude weight at zero magnetic field for the integrable
XXZ chain with arbitrary spin and easy-plane anisotropy. First, we construct
the fusion hierarchy of the quantum transfer matrices ($T$-functions) and
derive functional relations ($T$- and $Y$-systems) satisfied by the
$T$-functions and certain combinations of them ($Y$-functions). Through
analytical arguments, the $Y$-system is reduced to a set of non-linear integral
equations, equivalent to the thermodynamic Bethe ansatz (TBA) equations. Then,
employing GHD, we calculate the spin Drude weight at arbitrary finite
temperatures. As a result, a characteristic fractal-like structure of the Drude
weight is observed at arbitrary spin, similar to the spin-1/2 case. In our
approach, the solutions to the TBA equations (i.e., the $Y$-functions) can be
explicitly written in terms of the $T$-functions, thus allowing for a
systematic calculation of the high-temperature limit of the Drude weight.
