Profiles of the Palmer lines D-alpha(H-alpha), D-beta(H-beta) and D-gamma(H-gamma) have been measured in the scrape-off layer and within the edge of the TEXTOR (upgrade) plasma, under Ohmic conditions and with neutral-beam injection. Each line profile shows a strong Zeeman effect in the vicinity of line centre, and a marked central dip when mainly the sigma components are observed. The line core evidently originates from cold atoms in the edge plasma, excited in the course of molecular dissociation, while the broad pedestal on which the core rests is radiated by excited atoms produced through charge-exchange recombination of deuterons (protons), transported outwards from the much hotter plasma interior, and by atoms heated directly by collisions with the deuterons (protons). Core temperatures of about 0.5 eV and less are obtained from Line profile analysis.