There is provided an internal-combustion-engine ignition coil apparatus in which an igniter in a connector assembly is contained in the case of the ignition coil apparatus, in which an adhesive bonds the igniter to a heat sink inserted into the case through an opening window of the case and an adhesive bonds the heat sink to the inner circumferential surface of the opening window, and in which the exposed portion of the heat sink is exposed to the outside of the case through the opening window.