Heat conduction in composite solids is strongly dependent on the thermal contact conductance (TCC) between their different layers. The proper knowledge of TCC is very important in many engineering applications, such as electronic packaging, nuclear reactors, aerospace, and biomedicine applications, among others. A careful evaluation of TCC allows a more accurate analysis of a thermal system, in addition to allowing a qualitative assessment regarding the presence of discontinuities or failures within the material. Recently, the Reciprocity Functional Method (RFM), coupled with the Classical Integral Transform Technique (CITT), has been used as a tool for TCC estimation, as it allows the solution of inverse boundary value problems with a low computational cost, not requiring iterative methods nor intrusive measurements. The technique consists of defining two auxiliary problems: one for the temperature discontinuity and the other for the heat flux, both on the inaccessible interface between the two composite materials. In this work, the RFM and the CITT were used to estimate different types of TCCs, considering a double-layer hollow cylinder, which could represent, for instance, double-layer pipelines found in the oil industry. Temperature measurements for the inverse problem were considered available on the outer surface of the pipe, and the results shown high performance on several test cases. The influence of different measurement errors on the final solution was evaluated, showing the stability of the method.