A rheometer includes a drive shaft, a drag cup motor for rotating the drive shaft, a first measuring object supported by the drive shaft, a second measuring object, a linear position sensor, and processing and control electronics. The linear position sensor includes a target (e.g., an aluminum target) mounted to the drive shaft, and a pair of coils. The linear position sensor is configured to measure thermal expansion of the drive shaft based on a change in impedance of the coils resulting from a displacement of the target relative to the coils. The processing and control electronics are in communication with the coils and are configured to adjust a position of one of the measuring objects relative to the other based on a change in impedance of the coils resulting from a displacement of the target relative to the coils, thereby to maintain a substantially constant measurement gap therebetween.