  We use inelastic neutron scattering to study the temperature dependence of
the low-energy spin excitations in single crystals of superconducting
FeTe$_{0.6}$Se$_{0.4}$ ($T_c=14$ K). In the low-temperature superconducting
state, the imaginary part of the dynamic susceptibility at the electron and
hole Fermi surfaces nesting wave vector $Q=(0.5,0.5)$,
$\chi^{\prime\prime}(Q,\omega)$, has a small spin gap, a two-dimensional
neutron spin resonance above the spin gap, and increases linearly with
increasing $\hbar\omega$ for energies above the resonance. While the intensity
of the resonance decreases like an order parameter with increasing temperature
and disappears at temperature slightly above $T_c$, the energy of the mode is
weakly temperature dependent and vanishes concurrently above $T_c$. This
suggests that in spite of its similarities with the resonance in electron-doped
superconducting BaFe$_{2-x}$(Co,Ni)$_x$As$_2$, the mode in
FeTe$_{0.6}$Se$_{0.4}$ is not directly associated with the superconducting
electronic gap.
