Heating elements need a rapid heating property and long-term cycle stability when subjected to extreme temperatures. Carbon nanotube-based films can be used as ideal heating units owing to their superior electrical and thermal properties. However, carbon nanotube polymer composites are not appropriate for extreme conditions such as high temperatures (300 °C) due to the poor thermal stability of the polymer matrix. In this study, we fabricated a carbon nanotube web film, comprising heating elements consisting of pure carbon nanotubes, through the direct spinning method. The carbon nanotube web film has a microscale thickness. The carbon nanotube web film showed flexibility at high temperatures, while a fracture occurred in the case of the carbon nanotube polymer composite. We conducted electrical heating experiments on the curved carbon nanotube web film to observe the heating uniformity and flexibility. The heating test is conducted on various curved form heaters. The carbon nanotube web film showed rapid heating properties and a uniform heat distribution (temperature departure of less than 3%) without thermal aggregation. The curved heating units can be utilized in various applications such as functional clothes and de-icing systems having curved surfaces.