Rotation of a linear and homogenous microelongated thermoelastic medium with a uniform angular velocity are discussed in the present paper. The studied problem was considered as a perfecting conducting medium which irradiated by a non-gaussian laser beam. The nonlocal thermoelasticity theory was motivated to discuss the model with the energy dissipation in Green-Naghdi type III. Fourier and Laplace transforms are used to obtain the solution of the problem and get the considered physical quantities. The comparisons were computed numerically and represented graphically with different cases. The obtained results are applicable in many fields as earthquake engineering, nuclear physics, and manufacturing. It is found that the obtained results are significant.