Provided is a curable organopolysiloxane composition which includes (A) an organopolysiloxane containing at least 2 alkenyl groups bonded to silicon atoms within each molecule, (B) an organohydrogenpolysiloxane containing at least 2 hydrogen atoms bonded to silicon atoms within each molecule, (C) gallium and/or an alloy thereof, with a melting point within a range from 0 to 70° C., optionally (D) a heat conductive filler with an average particle size within a range from 0.1 to 100 μm, (E) a platinum based catalyst, and (F) an addition reaction control agent. The composition is useful as a material capable of forming a layer with excellent thermal conductivity that is sandwiched between a heat generating electronic component and a heat radiating member.