In a nuclear reactor, the coolant temperatures at 4,000 channel outlets are important for risk assessment. Temperatures measurements are made at only one in nine channels, and predictions of the temperatures are required at the remaining channels. The measured temperatures do not exceed an upper limit imposed by control action. Their histogram therefore provides no direct information about the distribution above this limit of the temperatures at the remaining channels. We predict the unmeasured temperatures by spatial interpolation of a surface fitted to the measured temperatures and modeling of the distribution of the residuals from this fit.