Root morphology and anatomy are important plant traits that could potentially influence seedling vigour, resource acquisition and susceptibility to early‐season stress. Therefore, the objective of the current experiment was to evaluate the effects of cultivar and growth temperature on seedling root growth and anatomical characteristics in cotton. To address this objective, experiments were conducted with six modern cotton cultivars, expected to have differences in seedling vigour, grown under optimal (30/20°C) and suboptimal (20/15°C) day/night temperature regimes. Root morphology and taproot cross‐sectional anatomy were evaluated two weeks after planting. Cultivars with the most vigorously growing root systems produced 73% more secondary roots, 68% more total root length, 74% more surface area and 72% higher total root volume than the least vigorous cultivars. The cultivar with the greatest production of secondary roots also exhibited a somewhat uncommon hexarch arrangement of vascular bundles in taproot cross sections. Thus, we suggest that this difference in root anatomy may be a determinant of genotypic differences in lateral root development. In response to low temperature, taproot length, total root length, secondary root formation, root surface area and root volume declined substantially relative to optimal temperature conditions (35%–75% declines). This reinforces the need to ensure optimal temperature conditions at planting or to identify cultivars with improved performance under suboptimal early‐season conditions. Conversely, root diameter responded positively to low growth temperatures, and cold‐induced increases in root thickness were associated with increases in the number and cross‐sectional area of root cells.