The invention relates to a composition that can be thermally cured, containing relative to the total composition, a) 5 to 90% by weight of a diene-based polymer or copolymer containing an olefinic double bond and/or an aromatically substituted olefin, wherein the polymer or copolymer is liquid, or paste-like, at 22° C. and has a glass transition temperature between −30° C. and +15° C., measured according to a DSC method; b) a vulcanization system selected from the group consisting of: b1) sulfur, and one or more accelerator(s), b2) peroxidic or disulfidic vulcanization systems, b3) quinones, quinone dioximes, or dinitrosobenzene.