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.

21 pages, 2 figures