A one-part curable thermally conductive silicone grease composition comprising: (A) 100 parts by weight organopolysiloxane, having an aliphatic unsaturated hydrocarbon group bonded to at least one silicon atom per single molecule, with a viscosity at 25°C between 50 and 100,000 mPa · s; (B) a linear organohydrogen siloxane that includes hydrogen atoms bonded to at least two silicon atoms per single molecule, of such hydrogen atoms, on average, 0 or more and less than 3 hydrogen atoms are bonded to non-terminal silicon atoms, in an amount wherein the number of hydrogen atom groups bonded to silicon atoms in the (B) component divided by the number of aliphatic unsaturated hydrocarbon groups in the (A) component is between 0.2 and 3.0; (C) between 400 and 5,000 parts by weight of a thermally conductive filler wherein the filler is particles having an average particle diameter between 0.01 and 200 μm; (D) between 0.01 and 20 parts by weight of a microparticle catalyst, with an average particle diameter of between 0.01 and 10 μm, comprising a thermoplastic resin with a softening point between 40°C and 200°C, wherein a platinum-based catalyst is included at no less than 0.01 mass %, as platinum metal atoms; and (E) between 0.001 and 5 parts by weight of a curing control agent, wherein the composition is capable of taking a cured form having a complex modulus of elasticity between 0.01 MPa and 20 MPa at 25°C, such complex modulus of elasticity measured using a rheometer (MCR102) in the following manner: (a) heat the one-part curable thermally conductive silicone grease composition for five minutes at 120°C; (b) let the grease composition rest for one week at room temperature (25°C); (c) set a parallel plate with a diameter of 20 mm, with a gap of 1.0 mm; and (d) measure the elasticity with a strain of 1% and a frequency of 1 Hz at a desired temperature. (A) 100 parts by weight organopolysiloxane, having an aliphatic unsaturated hydrocarbon group bonded to at least one silicon atom per single molecule, with a viscosity at 25°C between 50 and 100,000 mPa · s; (B) a linear organohydrogen siloxane that includes hydrogen atoms bonded to at least two silicon atoms per single molecule, of such hydrogen atoms, on average, 0 or more and less than 3 hydrogen atoms are bonded to non-terminal silicon atoms, in an amount wherein the number of hydrogen atom groups bonded to silicon atoms in the (B) component divided by the number of aliphatic unsaturated hydrocarbon groups in the (A) component is between 0.2 and 3.0; (C) between 400 and 5,000 parts by weight of a thermally conductive filler wherein the filler is particles having an average particle diameter between 0.01 and 200 μm; (D) between 0.01 and 20 parts by weight of a microparticle catalyst, with an average particle diameter of between 0.01 and 10 μm, comprising a thermoplastic resin with a softening point between 40°C and 200°C, wherein a platinum-based catalyst is included at no less than 0.01 mass %, as platinum metal atoms; and (E) between 0.001 and 5 parts by weight of a curing control agent, (a) heat the one-part curable thermally conductive silicone grease composition for five minutes at 120°C; (b) let the grease composition rest for one week at room temperature (25°C); (c) set a parallel plate with a diameter of 20 mm, with a gap of 1.0 mm; and (d) measure the elasticity with a strain of 1% and a frequency of 1 Hz at a desired temperature. <EOS>