An apparatus and method for the horizontal conveying of a dry powder is provided, notably useful for conveying heat from a heat-producing operation to a heat-consuming operation. In this application, heat is conveyed by a hot powder flowing through a vertically vibrated duct, the intensity of the vibration being sufficient to place the powder in a liquid-like state. The flow of powder is accompanied by a fall in pressure, and there is included a step for raising the pressure of the powder.