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This study describes the development of an integrated aerothermoelastic computational framework. The framework consists of a Navier-Stokes aerodynamic solver based on the Stanford University multiblock (SUmb) code, a finite element structural solver for moderate deflection of composite doubly-curved shallow shell with thermal stress, and a finite element thermal solver for heat transfer in composite shallow shells with nonlinear material properties. The solvers are coupled using a partitioned scheme. An analytical approach is developed to determine the time accuracy and the so-called energy accuracy of a loosely-coupled scheme. The energy accuracy is connected to the time accuracy of damping of the predicted response, and thus connected to the accuracy of predicted critical flutter point. The aeroelastic behaviors of 2D and 3D panels are investigated using the computational framework. The 3D effect and Reynolds number is found to have significant influence on the critical flutter parameter, and limit cycle amplitude.