The article discusses controlling the power of moving heat sources to heat a rod as per given rules and trajectories. The heat source control values are determined based on temperature measurements taken at nearby measuring points. An optimization approach is suggested for feedback coefficients of heat sources and measurement points in a rod’s state. Current values of the powers of moving lumped sources are distributed along the rod in a certain neighbourhood of their current location. The problem of control synthesis is reduced into the parametric optimal control problem for a system with distributed parameters. To solve the problem using numerical methods, first-order optimization methods are proposed. Formulas were derived for the gradient of the objective functional, considering feedback parameters and the coordinates of measurement points. The test problem can be solved numerically using first-order optimization methods with the help of these formulas. The report will present the results of numerical experiments.