The invention relates to a braking system (1) including: a dynamic brake (10), including a hydraulic ram (11), including a cylinder (12), a piston (13) movable in the cylinder (12), and a chamber (14) capable of being filled to displace the piston within the cylinder and actuate the brake, a circuit (20) for feeding the brake, including a reservoir (21) a pump (22) and a brake feed line (26), a brake control device (30), including a fluid pressure regulating valve (32) in the brake chamber, and progressive control (31), the valve including a path connected to the feed line, a path connected to the reservoir, and a path connected to the brake chamber, and being designed to selectively connect the path connected to the chamber to one or the other of the other paths, to deliver a predetermined pressure into the chamber according to a degree of actuation of the control, the braking system being characterized in that it further includes a chamber cooling line (40), designed to renew the fluid contained in the chamber to ensure cooling of said chamber.