  The high-temperature phase of Yang-Mills theory in Landau gauge is studied
using Dyson-Schwinger equations. The propagators of the gluon and the
Faddeev-Popov ghosts are obtained at finite and infinite temperature, partially
analytically. The results are in good agreement with lattice results. It is
found that the infrared properties are only quantitatively affected by
temperature. The confinement of at least soft gluons transverse to the heat
bath is established, in accordance with the Kugo-Ojima and Gribov-Zwanziger
confinement scenarios. This is confirmed by investigating the corresponding
Schwinger functions. The hard modes are nearly inert even at temperatures of
the order of the phase transition temperature. In addition, the thermodynamic
potential is analyzed and solutions for 3d-Yang-Mills theory are obtained. It
is conjectured that Yang-Mills theory likely undergoes a first order phase
transition, which changes a strongly interacting system into another. The
phases differ mainly by the properties of the chromoelectric sector.
