This paper presents a linear-quadratic regulator (LQR) approach for solving inverse heat conduction problems (IHCPs) arising in production processes like chip removing or drilling. The inaccessibility of the processed area does not allow the measuring of the induced temperature. Hence the reconstruction of the heat source based on given measurements at accessible regions becomes necessary. Therefore, a short insight into the standard treatment of an IHCP and the related LQR design is provided. The main challenge in applying LQR control to the IHCP is to solve the differential Riccati equation. Here, a model order reduction approach is used in order to reduce the system dimension. The numerical results will show the accuracy of the approach for a problem based on data given by practical measurements.