This study investigates the three-dimensional thermoelastic response of a functionally graded viscoelastic cylindrical panel embedded with piezoelectric layers subjected to asymmetric thermal loading. Utilizing the Boltzmann integral model to capture the viscoelastic behavior and a power-law distribution for the relaxation modulus in the radial direction, the governing equations are formulated based on full three-dimensional elasticity theory. The piezoelectric effects and the functional gradation of materials are rigorously incorporated. A combination of Laplace transform, Fourier series expansion, and state-space method is employed for analytically solving the simply-supported boundary condition, while a semi-analytical differential quadrature method (DQM) is used for more complex boundary conditions. The accuracy of the proposed method is validated through comparison with existing literature and analytical results. Parametric studies explore the effects of support conditions, time constants, opening angles, piezoelectric layer thicknesses, and other key factors on the structural response, providing insights into the design of smart FG cylindrical systems.