Recent progress in intense pulse lasers may allow new high-brightness short-pulse x-ray sources such as Larmor radiation or strong radiation damping due to the high intensity laser field. These x-ray sources are useful for (1)the excitation sources of inner-shell ionization x-ray laser, (2)measurement of ultrafast processes, and (3)the demonstration of photo-ionized plasma. However, it is difficult to measure fs pulse x-ray sources because they are mixed with long pulse x-ray emission processes such as bremsstrahlung. In this paper, we show that we may determine the x-ray intensities or temperatures with the use of the x-ray emission from hollow atoms generated by x-ray sources. For these aims, we treat x-ray emissions from the inner-shell excited states and hollow atoms of S and Fe ions excited by the black-body radiation of x-ray sources. The initial state of ions is assumed to be the ground state of Ne-like ion. We consider photo-ionization, radiative transition, and auto-ionization processes. We have calculated these atomic data using Cowan code and have adapted the atomic data averaged over the quantum numbers of spin angular momentum, orbital angular momentum, and total angular momentum. We found that the ratio of the x-ray intensities from hollow atoms to those from inner-shell excited states becomes larger as the black body temperature (T_B) increases or the number of electrons in the ions decreases. This ratio may tell us T_B of x-ray sources. These will be useful for not only high intensity laser physics but also x-ray astrophysics.