Hyperboloid cooling towers are counted among the largest cast-in-place industrial structures. They are an essential element of cooling systems used in many power plants in service today. Their main structural component, a reinforced-concrete shell in the form of a one-sheet hyperboloid with bidirectional curvature continuity, makes them stand out against other towers and poses very high construction and service requirements. The safe service and adequate durability of the hyperboloid structure are guaranteed by the proper geometric parameters of the reinforced-concrete shell and monitoring of their condition over time. This article presents an original concept for employing terrestrial laser scanning to conduct an end-to-end assessment of the geometric condition of a hyperboloid cooling tower as required by industry standards. The novelty of the proposed solution lies in the use of measurements of the interior of the structure to determine the actual thickness of the hyperboloid shell, which is generally disregarded in geometric measurements of such objects. The proposal involves several strategies and procedures for a reliable verification of the structure's verticality, the detection of signs of ovalisation of the shell, the estimation of the parameters of the structure's theoretical model, and the analysis of the distribution of the thickness and geometric imperfections of the reinforced-concrete shell. The idea behind the method for determining the actual thickness of the shell (including its variation due to repairs and reinforcement operations), which is generally disregarded when measuring the geometry of such structures, is to estimate the distance between point clouds of the internal and external surfaces of the structure using the M3C2 algorithm principle. As a particularly dangerous geometric anomaly of hyperboloid cooling towers, shell ovalisation is detected with an innovative analysis of the bimodality of the frequency distribution of radial deviations in horizontal cross-sections. The concept of a complete assessment of the geometry of a hyperboloid cooling tower was devised and validated using three measurement series of a structure that has been continuously in service for fifty years. The results are consistent with data found in design and service documents. We identified a permanent tilt of the structure's axis to the northeast and geometric imperfections of the hyperboloid shell from -0.125 m to +0.136 m. The results also demonstrated no advancing deformation of the hyperboloid shell over a two-year research period, which is vital for its further use.