An inverse analysis utilizing the conjugate gradient method of minimization and the adjoint equation is used for simultaneously estimating the temperature-dependent thermal conductivity and heat capacity per unit volume of a material. No prior information is used for the functional forms of the unknown thermal conductivity and heat capacity in the present study, thus, it is classified as the Function estimation by inverse calculation. The accuracy of the inverse analysis is examined by using simulated exact and inexact measurements obtained within the medium. Results show that the CPU time used on a VAX-9420 computer is within 1.4-4.46 s for all the test cases considered here. Moreover, excellent estimations on the thermal properties can be obtained when a good initial guess of either thermal conductivity or heat capacity is given before the inverse calculations.