  Thermal emission from the accretion disc around a black hole can be
polarized, due to Thomson scattering in a disc atmosphere. In Newtonian space,
the polarization angle must be either parallel or perpendicular to the
projection of the disc axis on the sky. As first pointed out by Stark and
Connors in 1977, General Relativity effects strongly modify the polarization
properties of the thermal radiation as observed at infinity. Among these
effects, the rotation of the polarization angle with energy is particularly
useful as a diagnostic tool.
  In this paper, we extend the Stark and Connors calculations by including the
spectral hardening factor, several values of the optical depth of the
scattering atmosphere and rendering the results to the expected performances of
planned X-ray polarimeters. In particular, to assess the perspectives for the
next generation of X-ray polarimeters, we consider the expected sensitivity of
the detectors onboard the planned POLARIX and IXO missions. We assume the two
cases of a Schwarzschild and an extreme Kerr black hole with a standard thin
disc and a scattering atmosphere. We compute the expected polarization degree
and the angle as functions of the energy as they could be measured for
different inclinations of the observer, optical thickness of the atmosphere and
different values of the black hole spin. We assume the thermal emission
dominates the X-ray band. Using the flux level of the microquasar GRS 1915+105
in the thermal state, we calculate the observed polarization.
