CUORE is a proposed array of 988, 750 g, TeO2 crystal bolometers. The experiment has been approved by the Scientific Committee of Gran Sasso Laboratories and the special dilution refrigerator, that is intended to house the detector has been funded. The Experiment will search for the 0v‐Double Beta Decay of 130Te. As in all the proposed next generation Double Beta Decay Experiments, the main task is the reduction of the radioactive background. A peculiar property of thermal detectors is that they are active over the entire volume and therefore strongly subject to radioactive surface contaminations. Unlike radioactive bulk contaminations, that can be measured through High‐Purity Ge Detectors, radioactive surface contaminations are not easily measurable at very low levels. Different techniques were developed in order to reach the required sensitivity. Present results already achieved and studies that are underway are here presented and discussed.