  We derive annual skymaps of the proton temperature in the inner heliosheath
(IHS), and track their temporal evolution over the years from 2009 to 2016 of
Interstellar Boundary Explorer observations. Other associated thermodynamic
parameters also determined are the density, kappa, that is, the parameter that
characterizes kappa distributions, temperature rate, polytropic index, and
entropy. We exploit the theory of kappa distributions and their connection with
polytropes, to (i) express a new polytropic quantity {\Pi} that remains
invariant along streamlines where temperature and density may vary, (ii)
parameterize the proton flux in terms of the {\Pi} invariant and kappa, and
(iii) derive the temperature and density, respectively, from the slope and
intercept of the linear relationship between kappa and logarithm of {\Pi}. We
find the following thermodynamic characteristics: (1) Temperature sky-maps and
histograms shifted to their lowest values in 2012 and their highest in 2015;
(2) Temperature negatively correlated with density, reflecting the
subisothermal polytropic behavior; (3) Temperature positively correlated with
kappa, revealing characteristics of the mechanism responsible for generating
kappa distributions; (4) Processes in IHS are sub-isothermal tending toward
isobaric, consistent with previously published results; (5) Linear relationship
between kappa and polytropic indices, revealing characteristics of the particle
potential energy; and (6) Entropy positively correlated with polytropic index,
aligned with the underlying theory that entropy increases towards the
isothermal state where the kappa distribution reduces to the Maxwell Boltzmann
description.
