<p>Thermal deformation is a major cause of machining errors in modern machine tools. In addition to optimising the machine structure, correcting the axis position values in the numerical control is a common way of reducing these errors. Another solution is to directly influence the temperature field of the machine tool in the process. In order to achieve this, thermoelastic analysis and modelling of the system are required, as well as appropriate thermal actuation and measurement capabilities in order to facilitate a targeted intervention. The modal analysis of the thermal system, which allows the temperature field to be described by independent discrete states. This independency is the basis of the thermal modal control approach. This paper presents the concept of modal control with regard to its application to machine structures. Based on numerical and experimental analyses, this paper investigates the real-time estimation of thermal mode amplitudes, comparing the modal filter and the Luenberger observer. A main source of estimation errors lies the presence of thermal modes that are not considered in the control approach. For this reason, an optimisation criterion is defined to select a set of thermal modes that can be actuated and estimated with minimal interaction.</p>