We study the dependence of the superconducting gaps on both the disorder and the temperature within the two-band model for iron-based materials. In the clean limit, the system is in the s ± state with the sign-changing gaps. Scattering by nonmagnetic impurities leads to the change of sign of the smaller gap thus resulting in a transition from the s ± to the s ++ state with the sign-preserving gaps. We show here that the transition is temperature-dependent, thus, there is a line of s ± → s ++ transition in the temperature-disorder phase diagram. There exists a narrow range of impurity scattering rates, where the disorder-induced s ± → s ++ transition occurs at low temperatures, but then the low-temperature s ++ state transforms back to the s ± state at higher temperatures. With increasing impurity scattering rate, temperature of such s ++ → s ± transition shifts to the critical temperature T c and only the s ++ state is left for higher amount of disorder.Symmetry 2018, xx, 1 2 of 12 change sign between the hole and the electron Fermi surface pockets to compensate the sign of the interaction in the gap equation. The simplest solution is called the s ± state and corresponds to the A 1g representation with the gap having one sign at hole pockets and opposite sign at electron pockets. At the same time, bands near the Fermi level have a mixed orbital character. Therefore, orbital fluctuations enhanced by, for example, electron-phonon interaction may also lead to a superconductivity [14][15][16]. These two mechanisms of superconducting pairing differs by the dominating superconducting gap structure: sign-changing s ± state for the spin fluctuations and sign-preserving s ++ state for the orbital fluctuations. Alas, superconducting gap structure has not been convincingly determined in experiments yet. Nevertheless, series of experimental observation such as the spin resonance peak in inelastic neutron scattering [17][18][19][20], a quasiparticle interference in tunneling experiments [21][22][23][24], the NMR spin-lattice relaxation rate [25,26], and the temperature dependence of the penetration-depth [27][28][29] are conveniently explained assuming the s ± state.Scattering on nonmagnetic impurities has different effect on superconductors with different gap symmetries and structures. The pure attractive interaction, both in the intraband and interband channels, results in the s ++ state. Its reaction to the disorder is well known since the earlier studies of the conventional s-wave superconductivity [30,31] and the modern treatment of the s ++ state within the multiband models [32]. According to the so-called Anderson's theorem [30], in a single-band s-wave superconductor, a nonmagnetic disorder does not affect the superconducting critical temperature T c . In the case of unconventional superconductors, Anderson's theorem is violated and the critical temperature is suppressed by a nonmagnetic disorder [33] similar to the T c suppression according to the Abrikosov-Gor'kov theory for magnetic impurities [34]. However, series...