Long hollow cylinders are commonly utilized in various technological applications, including liquid and gas transmission. As a result, its value is growing, becoming increasingly important to many research efforts. Compared with thermal isotropic homogeneous cylinders, thermo-viscoelastic orthotropic cylinders have less relevant data. In this paper, a thermoelastic fractional heat conduction model was developed based on the Moore-Gibson-Thompson equation to examine the axial symmetry problem of a viscoelastic orthotropic hollow cylinder. Atangana and Baleanu derivative operators with nonsingular and nonlocal kernels were used in constructing the fractional model. The thermal properties of the cylinder materials are assumed to be temperature-dependent. The Laplace transform is applied to solve the system of governing equations. The numerical calculations for temperature, displacement, and stress components are performed by the effect of fractional order, rotation, and changing thermal properties of the cylinder. The results showed that due to the presence of fractional derivatives, some properties of the physical fields of the medium change according to the value of the fractional order.