A hair heating device for use with regard to a permanent wave, which may elevate the hair temperature in a uniform manner without applying an excessive amount of heat energy not only to the head at a time but also to the hair locally so that the hair may escape deterioration and discoloration, and a process for permanent or dyeing hair by the device. The hair heating device includes two swing arms in the form of an arch, which include heaters mounted on the inside thereof, a concentric reverse reduction gearing, and a motor for driving said gearing. The concentric reverse reduction gearing is provided with an output shaft member A and an output shaft member B arranged such that both the output shaft members may rotate in opposite directions. A transmission member of the swing arm is connected with the output shaft member A, while a second transmission member of the swing arm is connected with the output shaft member B. A process is provided for permanent or dyeing hair that may be carried out by applying heat to the hair using the hair heating device.