  Observations of slow magneto-acoustic waves have been demonstrated to possess
a number of applications in coronal seismology. Determination of the polytropic
index ($\gamma$) is one such important application. Analysing the amplitudes of
oscillations in temperature and density corresponding to a slow
magneto-acoustic wave, the polytropic index in the solar corona has been
calculated and based on the obtained value it has been inferred that thermal
conduction is highly suppressed in a very hot loop in contrast to an earlier
report of high thermal conduction in a relatively colder loop. In this study,
using SDO/AIA data, we analysed slow magneto-acoustic waves propagating along
sunspot fan loops from 30 different active regions and computed polytropic
indices for several loops at multiple spatial positions. The obtained $\gamma$
values vary from 1.04$\pm$0.01 to 1.58$\pm$0.12 and most importantly display a
temperature dependence indicating higher $\gamma$ at hotter temperatures. This
behaviour brings both the previous studies to agreement and perhaps implies a
gradual suppression of thermal conduction with increase in temperature of the
loop. The observed phase shifts between temperature and density oscillations,
however, are substantially larger than that expected from a classical thermal
conduction and appear to be influenced by a line-of-sight integration effect on
the emission measure.
