MgB is a multi-band superconductor, that is each Fermi surface has different superconducting energy gap. For MgB, sigma bond of boron is strong, and it induces large s-wave superconducting gap, and pi bond is weak and induces small s-wave gap. 
The quasiparticle states of the vortices of large gap are highly confined to the vortex core.
On the other hand, the quasiparticle states of small gap are loosely bound to the vortex core. Thus they can be delocalized and overlap easily between adjacent vortices. Such delocalization can strongly contribute to the thermal conductivity, which shows abrupt increase above H.