HI filaments are cold and associated with dark molecular gas. HI4PI
  based estimates of the local diffuse CO-dark H2 distribution
  Context. There are significant amounts of H2 in the Milky Way. Due to its
symmetry H2 does not radiate at radio frequencies. CO is thought to be a tracer
for H2, however CO is formed at significantly higher opacities than H2. Thus,
toward high Galactic latitudes significant amounts of H2 are hidden and called
CO-dark. Aims. We demonstrate that the dust-to-gas ratio is a tool to identify
locations and column densities of CO-dark H2. Methods. We adopt the hypothesis
of a constant E(B-V)/NH ratio, independent of phase transitions from HI to H2.
We investigate the Doppler temperatures TD, from a Gaussian decomposition of
HI4PI data, to study temperature dependencies of E(B-V)/NHI. Results. The
E(B-V)/NHI ratio in the cold HI gas phase is high in comparison to the warmer
one. We consider this as evidence that cold HI gas toward high Galactic
latitudes is associated with H2. Beyond CO-bright regions we find for TD < 1165
K a correlation (NHI + 2NH2 )/NHI prop -log T_D. In combination with a factor
XCO = 4.0 10 20 cm^-2 (K km s^-1 )-1 this yields for the full-sky NH /E(B-V)
sim 5.1 to 6.7 10^21 cm^-2 mag^-1, compatible with X-ray scattering and UV
absorption line observations. Conclusions. Cold HI with T_D < 1165 K contains
on average 46% CO-dark H2. Prominent filaments have TD < 220 K and typical
excitation temperatures Tex sim 50 K. With a molecular gas fraction of > 61%
they are dominated dynamically by H2.
