The Fresnel-Fizeau effect of transverse drag, in which the trajectory of a light beam changes due to transverse motion of the optical medium, is usually extremely small and hard to detect. We observe transverse drag in a moving hot-vapor cell, utilizing slow light due to electromagnetically induced transparency (EIT). The drag effect is enhanced by a factor 360,000, corresponding to the ratio between the light speed in vacuum and the group velocity under EIT conditions. We study the contribution of the thermal atomic motion, which is much faster than the mean medium velocity, and identify the regime where its effect on the transverse drag is negligible.