A three‐dimensional theoretical model based on first principles has been developed to predict the characteristics of mass, momentum, energy, and electrostatic potential transport in high‐pressure mercury arcs confined in a quartz arctube. The model is utilized to systematically investigate the impact of convection on the transport process by including and excluding the gravity effect. Strong three‐dimensional convection flows with multiple contrarotating vortices have been identified. These vortices substantially change the energy balance within the arc, causing highly nonuniform gas temperature distribution and lowering the maximum gas temperature. Geometrical modifications of the arctube such as wall contour curvature and electrode offsets do not change the strength of convection but can produce better overall temperature uniformity within the arctube by accommodating the upward‐moving tendency of temperature contours caused by convection. In agreement with the experimental measurement, the model predicts that the arctube curvature can cause large differences of wall temperature profiles, including shape, level, and locations of peak values.