The spatially dependent neutron temperature profile measured by flux perturbing activation probes is correlated with the actual one-dimensional profile via a new singular Fredholm integral equation of the second kind. In time-of-flight measurements, the integral equation reduces to a singular Volterra type. A distinct anomalous profile deformation effect is theoretically predicted to be associated with each of these two techniques. The analytical investigation of the anomalous effects for neutron rethermalization experiments established that their magnitude should be far less than the standard errors of the associated techniques of measurement.