A numerical algorithm was developed which estimates a state-dependent model parameter on the basis of transient state observation data. The algorithm was presented for the problem of estimating the temperature dependence of thermal diffusivity in a one-dimensional heat equation. The estimation problem was converted into a finite dimensional optimization problem by the least-squares formulation and B-splines representation of the parameter. Numerical experiments were performed using simulated observation data as well as the actual observation data obtained in a heat conduction experiment on rubber compound layers. The performance of the algorithm was discussed in relation to the effect of the parameter representation scheme, the quality and quantity of the data.