Conjugate heat transfer is a process which involves a coupling of conduction in the solid and convection in the fluid. Previously various investigations have been done in this field by considering only crisp parameters. But we may not ignore the uncertainty involved in this system. So to get more acceptable and reliable results we have taken the involved parameters as uncertainty in terms of fuzzy. Here we have presented a modified form of Fuzzy Finite Element Method (FFEM) to handle the titled problem. However FFEM involves the complicated operation of uncertain/ fuzzy numbers. So, these fuzzy numbers are first changed into intervals through alpha-cut and then it is converted into crisp form by a proposed procedure. This crisp representation is used as a tool to handle fuzzy finite element method. In order to demonstrate the proposed method, we have investigated a conjugate heat transfer problem for a square plate. Finally obtained results from the proposed method are compared with the crisp results and the variability of uncertainty is studied. (C) 2013 Elsevier Ltd. All rights reserved.