Temperature-dependent thermal conductivity k(T)and specific heat C(T)are estimated simultaneously.At first,k(T) and C(T)are rewritten as functions of position and time,k(x,t)and C(x,t),and the gradient of cost function is deduced with adjoint equation method(AEM).Temperature is divided into segments and thermal conductivity and specific heat are expressed as constant in each segment.Gradients of cost function with respect to k(T)and C(<T)are further deduced from gradients of cost function with respect to k(x,t)and C(x,t).With a typical inversion problem,it is shown that the inversion method is feasible,effective and not too sensitive to measurement noise.