The invention relates to adhesive silicone elastomer compositions which can be crosslinked by polyaddition. The composition, crosslinkable by polyaddition (hydrosilylation), comprises: .alpha./ at least one polyorganosiloxane (POS) bearing ethylenic and/or acetylenic unsaturations [POS with .ident.Si-(unsaturated) units]; .beta./ at least one polyorganosiloxane (POS) with .ident.Si--H units; .gamma./ a catalytic combination comprising .gamma..1 at least one metallic catalyst (preferably platinum based), .gamma..2 and at least one crosslinking inhibitor; .delta./ a filler; .epsilon./ at least one adhesion promoter; .rho./ at least one POS resin; .lamda./ at least one thermal resistance agent; and .phi./ optionally at least one other functional additive. Methods of making and using the subject composition are also described.