Thermal effects in core optics of gravitational wave interferometric detectors can represent a strong limitation to their operation and sensitivity. These effects have already been observed in the present detectors and will become more relevant in the future interferometers, due to the much higher circulating power in the Fabry-Perot (FP) cavities. It is, then, necessary to realize a Thermal Compensation System (TCS) to correct the thermal effects due to the ITF beam. TCS can introduce displacement noise by means of several mechanisms. It is necessary to reduce TCS noise at a level compliant...