  The phenomenon of the almost linear growth of the square root of spatial
string tension $\sqrt{\sigma_s(T)}= c_{\sigma} g^2 T$ and of the Debye mass
$m_D(T)$ was found both in lattice and in theory, based on the Field Correlator
Method (FCM). In the latter the string tension (both spatial and colorelectric)
is expressed as an integral of the two gluon Green's function calculated with
the same string tension: $\sigma= \int G^{(2g)}_{\sigma}$. This relation allows
to check the selfconsistency of the theory and at high T it allows also to
calculate $c_{\sigma}$ and hence $\sigma_s$. We calculate below in the paper
the corresponding coefficients $c_{\sigma}$ and $c_D$ numerically in the FCM
method and compare the results with lattice data finding a good agreement. This
justifies the use of the FCM in the space-like region and in high T
thermodynamics without extra parameters.
