We consider the problem of reconstructing a priori unknown distributed controls in parabolic systems from results of approximate measurements of states of the system's observed motion. The problem is solved in the dynamic variant, when a current approximation of the unknown control is found only from the measurements received no later than the current time. The problem under consideration is ill-posed. We propose to solve it by the method of dynamic regularization and construct new dynamic regularization algorithms, which provide a strengthened convergence of regularized approximations, in particular, their piecewise uniform convergence. A finite-dimensional approximation of the problem is carried out and results of numerical simulation are presented.