In the current paper it is presented and tested an innovative method for estimating internal heat transfer coefficients in ducts adopting only thermal measurements acquired on the external wall surface. This approach is based on the reciprocity functional analysis, which is a powerful non-intrusive inverse problem technique. The adoption of this technique is promising since it avoids intrusive measurements, it is fully non-iterative and the computational time and cost are very limited. In this paper, it is presented an extension of the classical reciprocity functional methodology in the sense that a fully analytical expression, obtained by the integral transform technique, is developed for estimating the internal heat transfer coefficient in a three-dimensional problem. Such methodology, avoiding the solution of linear systems, reduces the computational costs that are massive when the traditional approaches are applied to three dimensional problems. The proposed procedure is first validated adopting synthetic temperature data and then tested using real temperature measurements acquired by an infrared camera. The results highlight that the methodology is able to recover the unknown functions in a very short computational time with a good accuracy. (C) 2018 Elsevier Ltd. All rights reserved.