This work is aimed at numerical studies of inverse problems of experiment processing
(identification of unknown parameters of mathematical models from experimental data) based on
the balanced identification technology. Such problems are inverse in their nature and often turn out
to be ill-posed. To solve them, various regularization methods are used, which differ in regularizing additions and methods for choosing the values of the regularization parameters. Balanced
identification technology uses the cross-validation root-mean-square error to select the values of
the regularization parameters. Its minimization leads to an optimally balanced solution, and the
obtained value is used as a quantitative criterion for the correspondence of the model and the regularization method to the data. The approach is illustrated by the problem of identifying the
heat-conduction coefficient on temperature. A mixed one-dimensional nonlinear heat conduction
problem was chosen as a model. The one-dimensional problem was chosen based on the convenience of the graphical presentation of the results. The experimental data are synthetic data obtained
on the basis of a known exact solution with added random errors. In total, nine problems (some
original) were considered, differing in data sets and criteria for choosing solutions. This is the first
time such a comprehensive study with error analysis has been carried out. Various estimates of the
modeling errors are given and show a good agreement with the characteristics of the synthetic data
errors. The effectiveness of the technology is confirmed by comparing numerical solutions with
exact ones.