Glass fibers drawn from the melt cool primarily by convection, through a boundary-layer process that has been the subject of a number of theoretical studies. In the present work, the temperature distribution along such a fiber has been measured under a range of conditions in a laboratory-scale system. The measurements were made using a heated thermocouple technique, in which a thermocouple is electrically heated to a temperature near the local fiber temperature. The response of the thermocouple is observed upon slight contact with the fiber, with null response indicating temperature equality. Data were collected for diameters ranging from 20 to 50 mum and speeds from 1 to 6 m/s. A comprehensive analysis was performed to estimate the uncertainty in our experiments. The analysis shows that the 2sigma uncertainty is 15.3%. Comparison between the experimental data and existing theoretical predictions shows that integral-method analyses produce the correct trends, but have systematic disagreements with the data. The direction and magnitude of these disagreements are system-dependent. Potential causes may include fiber vibration, boundary-layer transition, and measurement uncertainties.