Typically, any forming performed at or above the lower critical transformation temperature is considered hot forming. Normally this temperature range can be as low as 1350 deg F to as high as 1900 deg F.
Directly after hot forming, you can either air cool the steel (as hot formed condition) or hold the steel at 1650 deg F or higher temperature to ensure complete austenitization, air cool, which would result in a normalization heat treatment or you could quench and temper. You have options.