During the operation of engineering structures made of natural stone, for industrial and civil purposes, an important parameter in monitoring their technical condition is the assessment of their reliability and safety under the influence of various external influences. In this case, high-quality monitoring of the stress–strain state of natural stone structures, its physical, mechanical and filtration properties, as well as internal structural features is necessary to study the possibility of replacing individual elements of objects that have lost their original characteristics. To assess the state of geomaterials, this article proposes using a complex of introscopic methods, including infrared radiometry and laser-ultrasound structuroscopy. An important aspect is the calculation based on the Green–Christoffel equation of the velocity of a quasi-longitudinal wave in limestone consisting of densely packed, chaotically oriented calcite grains with a small quartz content. For the first time, using laser-ultrasonic structuroscopy and standard methods for determining open porosity, both total and closed porosity were determined. This allowed us to find the values of specific heat capacities of dry and water-saturated samples. The obtained values are used to find the ratio of changes in the temperature of dry and water-saturated samples at the same stress values. The results obtained demonstrate the need to take into account changes in the intensity of thermal radiation of limestone with different moisture content under conditions of uniaxial compression, when identifying changes in the stress state of elements of stone structures in real conditions.