<p>To investigate thermoelastic, homogeneous, and isotropic nanobeams, this investigation introduces a novel two-temperature Green-Naghdi heat conduction model. The substrate for electrical current and voltage low is a graphene strip located at the proximal end of the nanobeam. The nanobeam has been thermally strained under simply supported boundary conditions with defined aspect ratios because of the thermal impact of the electrical current. The governing differential equations associated with the time variable were resolved using the Laplace transform method. The Laplace transform was employed to derive solutions. The numerical calculation of the Laplace transform inversions was conducted using Tzou’s approximation method, which is based on an iterative formula. The numerical results for the graphene nano-strip’s diverse electrical voltage and resistivity values, which are the primary objective of this work, have been illustrated using graphs that illustrate a variety of scenarios. All the functions of the analyzed nanobeam that have been examined have been demonstrated to be influenced by the electrical voltage, two-temperature parameter, and electrical resistivity. The resistivity and voltage of a graphene nano-electrical strip may serve as a tuner to regulate the energy and vibration of the nanobeam.</p>