NLTE effects in iron lines are carefully investigated for the sunspot umbral model of Maltby et. al. (1986). Our model atom is realistic: it has hundreds of levels including many high-excited ones among which infrared transitions take place. The self-consistent solution of the kinetic and radiative transfer equations is obtained using recently-developed multilevel transfer methods suitable for efficiently handling hundreds of radiative transitions in detail from the ultraviolet to the infrared. These NLTE multilevel transfer calculations allow us to investigate whether the currently-used LTE approximation is suitable for diagnosing the temperature structure of sunspots via Fe I lines.