Thermal errors in machine tools account for up to 70% of machining errors, making it critical. Thermal displacement estimation using a reduced-order model (ROM) correlates temperature inputs with tool center point (TCP) displacement, where regression coefficients represent temperature sensitivity at each measurement point. Increasing the number of temperature input points in the ROM improves accuracy, but no method exists for determining the optimal number and placement of measurement points. This study provides guidelines for optimal sensor placement. An objective function was designed to explore temperature sensor placement, balancing two key factors: (1) ensuring the accuracy of thermal error estimation and (2) mitigating the impact of variability in temperature measurements. The objective function was defined as a linear combination of the absolute sum of temperature-sensitivity, representing estimation accuracy, and the squared sum of temperature-sensitivity, representing measurement uncertainty. The search for optimal sensor placement was formulated as a minimization problem of this objective function. Temperature-sensitivity distributions were utilized to visualize sensitivity across different areas of the machine tool to explore sensor placement. A sensor placement was achieved by quantitatively evaluating and appropriately weighing the two factors, which balance estimation accuracy with robustness against measurement errors.