  The Nahm data of periodic instantons, often called calorons, with spatial
$C_N$-symmetries are considered, by applying Sutcliffe's ansatz for the
monopoles with $C_N$-symmetries. The bulk data of calorons are shown to enjoy
the periodic Toda lattice, and the solutions are given in terms of elliptic
theta functions. The case of N=3 calorons are investigated in detail. It is
found that the "scale parameters" of these calorons have upper bounds in their
values, so that they do not have the large scale, or monopole, limits. The
instanton limit of the $C_3$-symmetric caloron is obtained.
