  The complex path (or Hamilton-Jacobi) approach to Hawking radiation
corresponds to the intuitive picture of particles tunnelling through the
horizon and forming a thermal radiation. This method computes the tunnelling
rate of a given particle from its equation of motion and equates it to the
Boltzmann distribution of the radiation from which the Hawking temperature is
identified. In agreement with the original derivation by Hawking and the other
approaches, it has been checked case by case that the temperature is indeed
universal for a number of backgrounds and the tunnelling of particles from
spins $0$ to $1$ mostly, spins $3/2$ and $2$ in some instances. In this letter,
we give a general proof that the temperature is indeed equal for all (massless
and massive) particles with spins from $0$ to $2$ on an arbitrary background
(limited to be Einstein for spin greater than $1$) in any number of dimensions.
Moreover, we propose a general argument to extend this result to any spin
greater than $2$.
