The quasistatic thertnoelastic equations for radially monoclinic cylindrical shells are solved in closed form for arbitrary temperature distributions and boundary conditions. In addition to both mechanical and thermal material anisotropy, the effects of shear deformation are admitted in the governing shell field equations. The solution to the governing thermomechanical noncanonical field equations is obtained through the use of integral transformations employed in conjunction with the application of adjoint differential operators. To illustrate the substantial effects of mechanical and thermal material anisotropy, the results of several numerical experiments are studied in detail.