  The thermal conductivity kappa of the layered s-wave superconductor NbSe_2
was measured down to T_c/100 throughout the vortex state. With increasing
field, we identify two regimes: one with localized states at fields very near
H_c1 and one with highly delocalized quasiparticle excitations at higher
fields. The two associated length scales are naturally explained as multi-band
superconductivity, with distinct small and large superconducting gaps on
different sheets of the Fermi surface. This behavior is compared to that of the
multi-band superconductor MgB_2 and the conventional superconductor V_3Si.
