The article solves the problem of reconstructing an unknown constant thermal conductivity coefficient in the Cauchy problem and the initial-boundary value problem for one- and two-dimensional heat conduction equations. The authors present numerical algorithms for approximate determination of the thermal conductivity under the assumption that the exact solution \( u (t ^ *; x ^ *) \) (\( u (t ^ *; x ^ *; y ^ *)\) is known at some fixed point \( (t ^ *; x ^ *) \) or \( (t ^ *; x ^ *; y ^ *)\)) in the case of the one-dimensional and two-dimensional heat equations, respectively. The algorithms for solving inverse problems are based on the application of a continuous method for solving nonlinear operator equations in Banach spaces [I. V. Boikov, Differ. Equ. 48, No. 9, 1288–1295 (2012; Zbl 1267.47094); translation from Differ. Uravn. 48, No. 9, 1308–1314 (2012)]. The method is based on replacing the original nonlinear operator equation with an ordinary differential equation of a special form and its subsequent numerical solution. The article presents the results of computational experiments on the approximate determination of the thermal conductivity on model examples of the Cauchy problem and the initial-boundary value problem for one- and two-dimensional heat equations.