This paper attempts to focus on inverse steady state thermoelastic problem of thin rectangular plate by means of internal moving heat source. For a given problem known second kind boundary condition and initial condition is applied. This is analyzed and solved by applying Fourier cosine transform and Marchi-Fasulo transform to obtain temperature distribution and its results are is an infinite series. The various different transformation and boundary conditions have been used for solving this kind of determination. Temperature distribution, thermal deflection and different kind of stresses have been focused and elaborated by considering the condition of temperature. This work puts lights on evaluation of unknown function. The integral transform technique yields the solution of inverse problem.