The present invention relates to a thermally curable composition comprising: (a1) a solid rubber in an amount of 2.5% by mass or more, (a2) an olefinic double bond-containing polymer which is liquid or pasty at 22° C. in an amount of less than 5% by mass, (a3) a hydrocarbon resin in an amount of, in total with said component (a2), 5% by mass or more and 20% by mass or less, and (a4) a liquid polydiene in an amount of 15% by mass or more based on the total mass of the composition as a component (a); and at least one selected from the group consisting of the following (b1) to (b3): (b1) sulfur and one or more accelerator(s), (b2) peroxidic vulcanization system or disulfidic vulcanization system, and (b3) quinones, quinone dioximes or dinitrosobenzene, as a vulcanization system (b).