Longitudinal defects of the internal coated surface of a metal pipe can be evaluated in a fast, precise and cheap way from thermal measurements on the external surface. In this paper, we study two classes of real situations in which the thickness of the coating is much smaller than the thickness of the metal tube: the transportation of potable water and crude oil. A very precise and stable reconstruction of damages is obtained by means of perturbation methods. To do this, first we translate a composite (coating-plus-tube) boundary value problem in a virtual one on the metallic part only. The information about possible damages is now included in the deviations delta h of the effective heat transfer coefficient from a known background value. Finally, we determine delta h by means of Thin Plate Approximation. (C) 2017 Elsevier Ltd. All rights reserved.