An arrangement for supplying a medium to an exhaust line of a combustion engine. The arrangement comprises a first exhaust passage defined by at least a first wall surface of an element, and a dosing device supplying the medium to the first exhaust passage. The arrangement is adapted to maintaining a degree of heating of the first wall surface so that the latter will be at a higher temperature than the medium's vaporization point when the liquid medium is supplied in the first exhaust passage. Therefore, even the medium which reaches the first wall surface will vaporize in the first exhaust passage.