This research work deals with analyzing instability and nonlinear behaviors of piezoelectric thermal nano-bridges. An adjustable thermo-elastic model with the ability to control stability conditions is developed to examine the system behavior at different temperatures. To increase the performance range and improve system characteristics, a piezovoltage is applied and a spring is connected to the sliding end of the deformable beam as design parameters. The partial differential equations (PDEs) are derived using the extended Hamilton's principle and Galerkin decomposition is implemented to discretize the nonlinear equations, which are solved via a computational method called the step-by-step linearization method (SSLM). To improve the accuracy of the solution, the number of mode shapes and the size of voltage increments are analyzed and sufficient values are employed in the solution. The validity of the formulation and solution method is verified with experimental, analytical, and numerical data for several cases. Finally, the vibration and eigenvalue problem of the actuated nano-manipulator subjected to electrostatic and Casimir attractions are investigated. It is concluded that the fringing-fields correction changes the system frequency, static equilibrium, and pull-in characteristics significantly. The results are expected to be instrumental in the analysis, design, and operation of numerous adjustable advanced nano-systems.