<p>This paper addresses the time-optimal control problem for a fourth-order parabolic equation in a multidimensional rectangular domain. The existence of a generalized solution to the corresponding initial-boundary value problem is established. By applying spectral techniques, the control problem is reduced to a Volterra integral equation of the first kind. Sufficient estimates for the kernel of this integral equation are derived to ensure the existence and uniqueness of its solution. As a result, the admissibility of the control function is proved, and sharp estimates for the minimal time required to achieve a prescribed average thickness of the thin film are obtained.</p>