This article discusses the influence of feedback on the Moderator Temperature Coefficient (MTC) estimate by a noise analysis method. Until now feedback was considered to be negligible in the frequency band of interest. However measurements at a Belgian Nuclear Power Plant will be used to show that the influence of feedback on the MTC estimate is not negligible in the frequency band of interest. This makes the analysis difficult since the presence of feedback creates systematic errors in the MTC estimate unless special experimental conditions can be realized. The theoretical analysis will explain how the most used non-parametric estimation of the MTC is influenced by the presence of the feedback. For the explanation we will consider a simplified scheme of the MTC measurement setup with feedback. The theory will be verified by simulations in MATLAB. For the verification we consider a simplified system captured in a feedback loop. We will estimate the system for different situations. It will be seen that the non-parametric system estimate is only unbiased when the signal that is fed back to the input is negligible in comparison with the reference signal. Since the feedback is not negligible in practice, special experimental conditions are required to obtain an unbiased non-parametric MTC estimate.