Abstract: The invention relates to an adhesive composition that can be cross-linked by heating, said composition comprising between 20 and 85% of a polyurethane comprising 2 terminal groups of the hydrolysable alkoxysilane type of formula (I): wherein: R1 is a hydrocarbonated radical comprising between 5 and 15 carbon atoms; R2 is an alkylene radical comprising between 1 and 4 carbon atoms; R3 is an alkylene radical comprising between 1 and 3 carbon atoms; R4 and R5 are each an alkyl radical comprising between 1 and 4 carbon atoms; n is a whole number such that the average molar mass of the polyether block of formula —[OR2]n- is between 300 Da and 30 kDa; in is a whole number such that the average molar mass of the polymer of formula (I) is between 600 Da and 60 kDa; and p is a whole number equal to 0, 1 or 2. The composition also comprises between 15 and 80% of a compatible tackifying resin; and between 0.01 and 3% of a cross-linking catalyst.