A fractional four-step finite element method for analyzing conjugate heat transfer between solid and unsteady viscous flow is presented. The second-order semi-implicit Crank-Nicolson scheme is used for time integration and the resulting nonlinear equations are linearized without losing the overall time accuracy. The streamline upwind Petrov-Galerkin method (SUPG) is applied for the weighted formulation of the Navier-Stokes equations. The method uses a three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the method presented is to consistently couple heat transfer along the fluid-solid interface. Five test cases, which are the lid-driven cavity flow, natural convection in a square cavity, transient flow over a heated circular cylinder, forced convection cooling across rectangular blocks, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the method presented.