A thermally conductive silicone rubber composition comprising: 100 parts by mass of an organopolysiloxane that contains at least two silicon-bonded alkenyl groups in each molecule, that does not contain a silicon-bonded hydroxyl group and does not contain a silicon-bonded alkoxy group, and that has a content of cyclic siloxanes having from 4 to 20 siloxane units of not more than 1,000 ppm in mass units; an organopolysiloxane that contains at least two silicon-bonded hydrogen atoms in each molecule and that does not contain a silicon-bonded alkenyl group, does not contain a silicon-bonded hydroxyl group, and does not contain a silicon-bonded alkoxy group, in an amount that provides from 0.5 to 10 moles of silicon-bonded hydrogen atoms in this component per 1 mole of the alkenyl groups in component; at least 0.05 parts by mass of an adhesion promoter, wherein the adhesion promoter is a mixture of the following components (i) and (ii) or a condensation reaction product from the following components (i) and (ii), wherein (i) is an organosilicon compound that contains a silicon-bonded alkoxy group and that has a boiling point of at least 100°C; and (ii) is a diorganosiloxane oligomer that contains a silicon-bonded hydroxyl group and at least one silicon-bonded alkenyl group in each molecule; 100 to 2,000 parts by mass of a thermally conductive filler that is surface treated in situ with a silicon-type surface-treatment agent by blending component into a mixture of component and methyltrimethoxysilane; or by blending methyltrimethoxysilane into a mixture of component and component; and a catalytic quantity of a hydrosilylation reaction catalyst; wherein the total quantity of components and is from 0.5 to 10 mass% of the total quantity of components,, and. 100 parts by mass of an organopolysiloxane that contains at least two silicon-bonded alkenyl groups in each molecule, that does not contain a silicon-bonded hydroxyl group and does not contain a silicon-bonded alkoxy group, and that has a content of cyclic siloxanes having from 4 to 20 siloxane units of not more than 1,000 ppm in mass units; an organopolysiloxane that contains at least two silicon-bonded hydrogen atoms in each molecule and that does not contain a silicon-bonded alkenyl group, does not contain a silicon-bonded hydroxyl group, and does not contain a silicon-bonded alkoxy group, in an amount that provides from 0.5 to 10 moles of silicon-bonded hydrogen atoms in this component per 1 mole of the alkenyl groups in component; at least 0.05 parts by mass of an adhesion promoter, wherein the adhesion promoter is a mixture of the following components (i) and (ii) or a condensation reaction product from the following components (i) and (ii), wherein (i) is an organosilicon compound that contains a silicon-bonded alkoxy group and that has a boiling point of at least 100°C; and (ii) is a diorganosiloxane oligomer that contains a silicon-bonded hydroxyl group and at least one silicon-bonded alkenyl group in each molecule; (i) is an organosilicon compound that contains a silicon-bonded alkoxy group and that has a boiling point of at least 100°C; and (ii) is a diorganosiloxane oligomer that contains a silicon-bonded hydroxyl group and at least one silicon-bonded alkenyl group in each molecule; 100 to 2,000 parts by mass of a thermally conductive filler that is surface treated in situ with a silicon-type surface-treatment agent by blending component into a mixture of component and methyltrimethoxysilane; or by blending methyltrimethoxysilane into a mixture of component and component; and a catalytic quantity of a hydrosilylation reaction catalyst;