The inherent temperature-dependent sublattice preference of constituent atoms in FCC_CoCuNi multi-principal element alloys (MPEAs) is theoretically predicted by combining a two-sublattice model based on the L12_AuCu3 prototype with computational thermodynamics, which extends beyond the commonly-believed, yet unreasonable randomly mixing solid solution hypothesis. Based on the predicted sublattice occupied fractions (SOFs) and available computer resource, two MPEAs atom distributing models with different sizes are established for different applications, respectively, where the bigger size model is further employed to analyze statistically the atom distributing character quantitatively and graphically, while the smaller size model is employed to study the lattice distortion of MPEAs further using first-principles calculations density functional theory. The atom distributing configurations of some representative heat treatment temperatures, as well as the hypothetical randomly mixing structure are compared. It is revealed that FCC_CoCuNi MPEAs exhibit strong temperature-dependent ordering behavior. The SOFs-based configurations are (Ni1.0000)1a(Co0.4445Cu0.4444Ni0.1111)3c, (Co0.0653Cu0.0721Ni0.8626)1a(Co0.4227Cu0.4204Ni0.1569)3c, and (Co0.1574Cu0.1593Ni0.6833)1a(Co0.3920Cu0.3913Ni0.2167)3c at 100 K, 900 K, and 1400 K, respectively. Overall, Ni atoms always prefer to 1a sublattice and the preference tendency reduce a little bit at considerable high temperatures. The configurational entropies of FCC_CoCuNi MPEAs increase with the increase of heat treatment temperature, while they are considerably lower than that of the hypothetical ideal random solid solution. Based on the atom distributing model of MPEAs, the local atomic cluster characteristics are further investigated by statistically analyzing the coordination numbers of the constituent atom coordinated with the same type of atoms. The radial distribution function (RDF) further verified the atom aggregating behavior. For most family of crystal planes in FCC_MPEAs, except {1 1 1}, there are obviously different atom distributing characters between the even and odd layers. The atom distributing model of some representative bulk structure and surface structure are afforded valuably for reference and application both in experimental and theoretical investigation further. Thus, rich and indispensable structural genome data are afforded for the further research and development of the promise FCC_CoCuNi MPEAs intensively.