An anterior part of a nacelle of a propulsion assembly of an aircraft, having an air intake lip and a front frame disposed at the rear of the air intake lip that connects an outer part to an inner part of the air intake lip. A de-icing duct is formed in front of the front frame. The front frame is shaped so that the de-icing duct has a main cavity and a thermal transition region formed behind the main cavity between an internal face of the outer part of the air intake lip and the front frame. The thermal transition region extends over a longitudinal dimension greater than its average radial dimension, the front frame forming, with respect to the internal face of the outer part of the air intake lip, an angle, measured longitudinally, of between −20° and +10° over the majority of the thermal transition region.