Flow passages associated with internal cooling of high temperature engine components, especially those in gas turbine engines, frequently have very complex surface geometries. The flow channels usually are roughened to enhance heat transfer rates, and often incorporate sharp turns. The acquisition of detailed local heat transfer coefficient distributions over complex surface geometries is often extremely difficult or prohibitively expensive using conventional techniques. A relative new method of acquiring heat transfer coefficients through use of surface coatings that have precise melting points is described. As an example of the use of the technique, it is applied to the study of the effect of various rib roughness patterns on heat transfer through 90° turns in a rectangular cooling channel.