This paper is concerned with the determination of unknown temperature The present study considers a semi-infinite hollow circular disk subjected to internal heat generation. Initially, the disk possesses an arbitrary temperature distribution denoted by F(r,z). For time t > 0, heat is generated within the domain at a rate g(r,z,t) Btu/hr·ft³. Thermal flux is imposed along both the inner and outer cylindrical boundaries. The lower surface of the disk is maintained at a prescribed temperature f3(r,t) , while the upper surface is kept at zero temperature. The disk extends infinitely in the positive z-direction, starting from z=0. The governing equations describing the thermoelastic behavior of the system are solved using the finite Hankel transform in the radial direction and the finite Fourier transform in the axial direction. The resulting temperature distribution is expressed in a series representation involving Bessel functions.