  Using variational matrix product states, we analyze the finite temperature
behavior of a half-filled periodic Anderson model in one dimension, a
prototypical model of a Kondo insulator. We present an extensive analysis of
single-particle Green's functions, two-particle Green's functions, and
transport functions creating a broad picture of the low-temperature properties.
We confirm the existence of energetically low-lying spin excitations in this
model and study their energy-momentum dispersion and temperature dependence. We
demonstrate that charge-charge correlations at the Fermi energy exhibit a
different temperature dependence than spin-spin correlations. While
energetically low-lying spin excitations emerge approximately at the Kondo
temperature, which exponentially depends on the interaction strength, charge
correlations vanish already at high temperatures. Furthermore, we analyze the
charge and thermal conductivity at finite temperatures by calculating the
time-dependent current-current correlation functions. While both charge and
thermal conductivity can be fitted for all interaction strengths by gapped
systems with a renormalized band gap, the gap in the system describing the
thermal conductivity is generally smaller than the system describing the charge
conductivity. Thus, two-particle correlations affect the charge and heat
conductivities in a different way resulting in a temperature region where the
charge conductivity of this one-dimensional Kondo insulator is already
decreasing while the heat conductivity is still increasing.
