High precision machines require very stable operational environment: temperature control and vibration isolation. Tight temperature control for machines usually demand high cost to operate air conditioners. Some of high precision machines require the ambient temperature changes to maintain within ${pm}0.1$ degrees. In this paper, we present a thermal error compensation scheme and experimental results for improving machining accuracy of a high precision lathe. The testbed lathe has X- and Z-axes and they are driven by linear motors and hydrostatic oil bearing. Due to the temperature changes of the ambient air and supplied oil to the hydrostatic bearing, thermal deformation is generated and measured to be as much as 200-300 nm. To identify the dynamic relations between the temperature changes and the thermal drift, a state-space model is used in which state variables are constructed from the input measured temperatures and the output thermal drift data. The identified model is implemented in a servo control loop and the predicted thermal error is compensated by subtracting the predicted thermal drift from the servo command. In our simulation, a thermal error of 97 nm rms over 3 hours is reduced to 55 nm rms. Experimental results showed an 30% ~ 60% reduction in thermal drift and supported the validity of our approach.