  We investigate the thermal topology in a super-penumbral canopy by
determining the 3D thermal structure of an active region. We derive the
temperature stratifications in the active region by an inversion of the Ca II
IR line at 854.2 nm, assuming LTE. We trace the 3D topology of individual
features located in the super-penumbral canopy, mainly radially oriented
fibrils. We find that about half of the fibrils form short, arched, low-lying
loops in the temperature cube. These closed loops connect from bright grains
that are either in or close to the penumbra to the photosphere a few Mms away
from the sunspot. They reach less than 1 Mm in height. The other half of the
fibrils rise with distance from the sunspot until they leave the Ca II IR
formation height. Many of the fibrils show a central dark core and two lateral
brightenings as seen in line-core intensity images. The corresponding velocity
image shows fibrils that are as wide as the fibrils seen in intensity without a
lateral substructure. Additionally, we study one example of exceptional
brightness in more detail. It belongs to a different class of structures
without prominent mass flows and with a 3D topology formed by two parallel,
closed loops connecting patches of opposite polarity. We present evidence that
the inverse Evershed flow into the sunspot in the lower chromosphere is the
consequence of siphon flows along short loops that connect photospheric foot
points. The dark-cored structure of the chromospheric fibrils cannot have an
convective origin because of their location above regular granulation in an
optically thin atmosphere. The dark core most likely results from an opacity
difference between the central axis and the lateral edges caused by the
significant flow speed along the fibrils.
