In a process for dyeing a textile web having a first face and a second face opposite the first face, a solvent-based dye having at least one component that has a thermal conductivity substantially greater than that of the solvent is applied to the textile web. The web is then moved, in an open configuration thereof, over a contact surface of an ultrasonic vibration system with the textile web in direct contact with the contact surface of the ultrasonic vibration system. The ultrasonic vibration system is operated to impart ultrasonic energy to the textile web at the contact surface of the ultrasonic vibration system. In one embodiment, the dye is applied to the first face of the web and the web is then moved over the contact surface of the ultrasonic vibration system with the second face of the web in direct contact with the contact surface.