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In this paper, a transient thermal stress investigation on a simply supported thin elliptical plate during sectional heating with time-dependent temperature supply is considered. The solution of heat conduction equation with corresponding initial and boundary conditions is obtained by employing an integral transform approach. The governing equation solution for the small deflection theory is obtained and utilized to preserve the intensities of thermal bending moments, involving the Mathieu and modified functions and its derivatives. The deflection results show an approximately good agreement with the previously given results. It is also demonstrated that the temperature field in a circular solution could be resulted in a particular case of the present mathematical solution. The obtained numerical results utilizing computational implements are precise enough for practical purposes.