A numerical experiment was used to evaluate the properties of an upwind differencing scheme for a circular roll rotating at high velocity. Since the roll is rapidly rotated, the temperatures vary only within a thin layer near the outer roll surface, which results in a situation that is numerically favorable for the upwind scheme. Comparison of the present upwind results with a known analytical solution indicates that, with the same number of grid points, better accuracy is achieved at higher Peclet numbers. The present study also indicates that the numerical accuracy is greatly affected by changing mesh size in the radial direction, but is not noticeably affected by changing it in the circumferential direction for the range considered. Some specific features associated with the thermal behavior of a high-speed rotating roil are also presented to explain the numerical findings.