A thermoplastic polymer having good tensile strength at elevated temperatures is obtained by modifying a block copolymer composed of a conjugated diene compound and an alkenyl arene compound. The block copolymer is first selectively hydrogenated and thereafter modified by grafting silicon or boron containing functional groups primarily in the alkenyl arene block via metalation. Each silicon containing functional group preferably contains at least two functional groups which allow crosslinking by condensation reactions.