The uniquess of the effective actions describing 4D SU(2) and SU(3) continuum, infinite-volume Yang-Mills thermodynamics in their deconfining and preconfining phases is made explicit. Subsequently, the spatial string tension is computed in the approach proposed by Korthals-Altes. This SU(2) calculation is based on a particular, effective two-loop correction to the pressure needed for the extraction of the hypothetic number density of isolated and screened magnetic monopoles or antimonopoles in the deconfining phase. By exponentiating the exchange of the tree-level massless but one-loop dressed mode within a quadratic spatial contour of side-length L in the effective theory we demonstrate that for L [RIGHTWARDS ARROW] ∞ the Wilson loop exhibits perimeter law. This is in contrast to a rigorous lattice result subject to the Wilson action and for this action valid at sufficiently high temperature. In the framework of the effective theory there is, however, a regime for small (spatially unresolved) L were the exponent of the spatial Wilson loop possesses curvature as a function of L.