  We apply the concept of reflection-transmission (RT) algebra, originally
developed in the context of integrable systems in 1+1 space-time dimensions, to
the study of finite temperature quantum field theory with impurities in higher
dimensions. We consider a scalar field in $(s+1)+1$ space-time dimensions,
interacting with impurities localized on $s$-dimensional hyperplanes, but
without self-interaction. We discuss first the case $s=0$ and extend afterwards
all results to $s>0$. Constructing the Gibbs state over an appropriate RT
algebra, we derive the energy density at finite temperature and establish the
correction to the Stefan-Boltzmann law generated by the impurity. The
contribution of the impurity bound states is taken into account. The charge
density profiles for various impurities are also investigated.
