Illustration of the determination of the temperature for three 400SD clusters. The dashed line is the ƒ₁(T) function, the luminosity corresponding to the temperature, T, given the L₅₀₀-T relation, divided by the luminosity $\left(4\pi D_1^2(ɀ)F_{\text{ap}}\right)$ estimated from the input aperture flux without correction (Eq. B.9). The solid line is the correction function ƒ₂(T) defined in Eq. B.10, the product of the K-correction, the K_L correction factor used to convert the luminosity from the [0.5–2.] keV input band to [0.1-2.4] keV band and F_ap is the aperture correction (fixed in that case). Both functions depend on cluster redshift. The curves are color-coded in blue, green and red for the MCXC J1116.9+1803 (z = 0.0032), MCXC J1823.7+5658 (z = 0.1050), and MCXC J1226.9+3332 (z = 0.888), respectively. The temperature is the intersection of the two curves (points). Starting from T = 3 keV, the iterative trajectory is shown in a thin blue line with arrows for the cluster MCXC J1116.9+1803 (z = 0.0032). We note the rapid convergence.