One of the major limitations of productivity and quality in metal cutting is the machining accuracy of machine tools. The machining accuracy is affected by geometric errors, thermally-induced errors, and the deterioration of the machine tools. Geometric and thermal errors of machine tools should be measured and compensated to manufacture high quality products. In metal cutting, the machining accuracy is more affected by thermal errors than by geometric errors. This paper models of the thermal errors for error analysis and develops on-the-machine measurement system by which the volumetric error are measured and compensated. The thermal error is modeled by means of angularity errors of a column and thermal drift error of the spindle unit which are measured by the touch probe unit with a star type styluses and a designed spherical ball artifact (SBA). Experiments, performed with the developed measurement system, show that the system provides a high measuring accuracy, with repeatability of $pm$2${mu}{ extrm}{m}$ in X, Y and Z directions. It is believed that the developed measurement system can be also applied to the machine tools with CNC controller. In addition, machining accuracy and product quality can be improved by using the developed measurement system when the spherical ball artifact is mounted on the modular fixture.