  The ensemble geometric phase (EGP) has been proposed as a topological
indicator for finite-temperatures systems. The ensemble Wilson loop, or the
transfer matrix, contains the crucial information in the EGP construction. We
propose a proxy index and a proxy EGP directly from the transfer matrix and
apply them to time-reversal invariant topological insulators exemplified by the
Bernevig-Hughes-Zhang (BHZ) and Kane-Mele (KM) models. The quantized proxy
index and proxy EGP smoothly generalize the ground-state topological index to
finite temperatures. For the BHZ model, a comparison with another topological
indicator, the Uhlmann phase, shows different transition behavior with
temperature. For the KM model, the EGP have been generalized to the
time-reversal EGP previously, but the proxy EGP does not require any splitting
of the contributions. The proxy index and proxy EGP thus offer an efficient
means for characterizing finite-temperature topological properties.
