The main measure to reduce energy losses is the usage of insulating materials. When the temperature exceeds 500 °C, silicate and ceramic products are most commonly used. In this work, high-crystallinity 1.13 nm tobermorite and xonotlite were hydrothermally synthesized from lime and Ca–Si sedimentary rock, opoka. By XRD, DSC, TG and dilatometry methods, it has been shown that 1.13 nm tobermorite becomes the predominant compound in stirred suspensions at 200 °C after 4 h of synthesis in the mixture with a molar ratio CaO/SiO2 = 0.83. It is suitable for the production of insulating products with good physical–mechanical properties (average density < 200 kg·m−1, compressive strength ~0.9 MPa) but has a limited operating temperature (up to 700 °C). Sufficiently pure xonotlite should be used to obtain materials with a higher operating temperature. Even small amounts of semi-amorphous C–S–H(I) significantly increase its linear shrinkage during firing. It has also been observed that an increase in the strength values of the samples correlated well with the increase in the size of xonotlite crystallites. The optimal technological parameters are as follows: molar ratio of mixture CaO/SiO2 = 1.2; water/solid ratio W/S = 20.0; duration of hydrothermal synthesis at 220 °C—8 h, duration of autoclaving at 220 °C—4 h. The average density of the samples was ~180 kg·m−1, the operating temperature was at least 1000 °C, and the compressive strengths exceeded 1.5 MPa.