Thermal contact conductance (TCC) is a critical factor in various engineering applications involving heat transfer between solid surfaces. Accurate knowledge of TCC enables a more precise thermal system analysis, leading to improved efficiency, reduced energy consumption, and prevention of thermal damages. Moreover, TCC estimation can help to identify material discontinuities or failures. A recent tool for TCC estimation is the Reciprocity Functional Method (RFM) coupled with the Classical Integral Transform Technique (CITT). This method allows the solution of inverse boundary value problems without the need of iterative methods or intrusive measurements, making it valuable for nondestructive testing of interfacial flaws between solid materials. Furthermore, it enables the computation of TCCs using analytical expressions, resulting in a computationally fast procedure. The technique involves the solution of two auxiliary problems: one for the temperature discontinuity estimation, and the other for the interfacial heat flux estimation, both at the inaccessible interface between the two contacting materials. In this study, we applied the RFM and the CITT to estimate different types of TCCs, using a three-dimensional double-layer hollow cylinder geometry as a representative model, like double-layer pipelines used in the oil industry. Temperature measurements for solving the inverse problem were considered available on the outer surface of the pipe which, in the case of a real experiment, could be obtained via an infrared camera. The results demonstrated a good estimate for various analyzed test-cases, even when the measurements were contaminated with Gaussian noises.