In the framework of the fractional-order Caputo-Fabrizio differential, the mathematical modelling is established for a thick cylindrical body under the influence of a heat source. The Robin conditions for the limits of heat exchange on the curved outer surface are set to zero, while additional cross-sectional heating has been applied to the top and bottom surfaces of the body. The governing equation for the mathematical modelling is solved analytically and evaluated computationally using the integral transformation technique. The results obtained from the thermal variations are presented graphically and illustrated numerically, assuming the material properties of aluminium metal.