  We perform numerical renormalization group (NRG) as well as analytical
calculations for the two-channel Kondo model to obtain the dependence of the
Kondo temperature $T_K$ on the dimensionless (bare) spin exchange coupling $g$
over the complete parameter range from $g\ll 1$ to $g\gg 1$. We show that there
exists a duality between the regimes of small and large coupling. It is unique
for the two-channel model and enables a mapping between the strong and the weak
coupling cases via the identification $g\leftrightarrow 3/(2g)$, implying an
exponential dependence of $T_K$ on $1/g$ and $g$, respectively, in the two
regimes. This agrees quantitatively with our NRG calculations where we extract
$T_K(g)$ over the complete parameter range and obtain a non-monotonous $T_K(g)$
dependence, strongly peaked at the 2CK fixed point coupling $g^*$. These
results may be relevant for resolving the long-standing puzzle within the 2CK
interpretation of certain random defect systems, why no broad distribution of
$T_K$ is observed in those systems.
