  We study $\mathcal{W}_3$ toroidal conformal blocks for degenerate primary
fields in AdS/CFT context. In the large central charge limit $\mathcal{W}_3$
algebra reduces to $\mathfrak{sl}_3$ algebra and $\mathfrak{sl}_3$ blocks are
defined as contributions to $\mathcal{W}_3$ blocks coming from the generators
of $\mathfrak{sl}_3$ subalgebra. We consider the construction of
$\mathfrak{sl}_3$ toroidal blocks in terms of Wilson lines operators of $3d$
Chern-Simons gravity in the thermal AdS$_3$ space-time. According to the
correspondence, degenerate primary fields are associated with Wilson lines
operators acting in the corresponding finite-dimensional $\mathfrak{sl}_3$
representations. We verify this dual construction for one-point toroidal block
using $\mathfrak{sl}_3$ tensor technique in the bulk theory and an algorithm
based on AGT correspondence in the boundary CFT.
