A simply supported rectangular plate of small thickness with a thermal bending moment is considered in this proposed work, and fractional order theory is used to analyze the thermo-elastic effects. A point heat source that is instantly available and situated anywhere inside the solid rectangular plate is also present. The influences of thermally stressed components are evaluated for weak, moderate, and superconductivity using the thermal moment of bending. The outcomes are achieved as a series solution, and the corresponding convergences have been illustrated. For computational analysis, copper-based material properties of a rectangular plate shape are assumed, and graphically plotted results are presented successfully. In the above-mentioned study, we prepared the mathematical model for defined parameters and functions and illustrated the result with physical significance. Till date, only studies have shown the thermal bending moment for classical heat conduction equations, whereas this work, considered heat conduction containing a fractional order approach, which predicts the retarded response, and it also interpolates classical heat conduction equations. As a part of the comparison, the limiting case is discussed.