  Yang-Mills theories undergo a deconfining phase transition at a critical
temperature. In lattice calculations the temporal Wilson loop and Z_3 order
parameter show above this temperature a behavior typical of deconfinement. A
quantity of interest in the study of this transition is the gluon propagator
and its evolution with temperature. This contribution describes the current
status of an investigation of the finite temperature gluon propagator in Landau
gauge. It analyzes the high temperature case. The resulting equations are
compared to the corresponding ones of three-dimensional Yang-Mills theory.
Under certain assumptions it is found that a kind of spatial "confinement" is
still present, even at very high temperatures.
