  The phenomenon of Heider (structural) balance is known for a long time (P.
Bonacich and P. Lu, Introduction to Mathematical Sociology, Princeton UP,
2012). Yet it attracts attention of numerous computational scholars, as it is
an example of a macroscopic ordering which emerges as a consequence of local
interactions. In this paper, we investigate the thermal evolution (driven by
thermal noise level $T$) of the work function $U(T)$ for Heider balance on
several Archimedean lattices that contain separated triangles, pairs of
triangles, chains of triangles and complex structures of triangles. To that
end, the heat-bath algorithm is applied. Two schemes of link values updating
are considered: synchronous and asynchronous. In the latter case, the
analytical formula $U(T)=-\tanh(1/T)$ based on the partition function is
provided. The Archimedean lattices are encoded with adjacency matrices, and
Fortran procedures for their construction are provided. Finally, we present the
mathematical proof that for any two-dimensional lattice, perfect structural
(Heider) balance is unreachable at $T>0$.
