A method is disclosed for making a heat dissipation arrangement for a circuit board on which are mounted bare silicon chips having an exposed face. A heat spreader has a planar portion, on whose inner face (facing the circuit board) are applied one or more pads of a gel composition. The pad(s) are positioned opposite the bare silicon chips when the heat spreader is attached to the circuit board and completely cover the exposed faces of the chips. The gel composition has a cohesive strength greater than its adhesive strength, has a compression modulus of less than 1.38 MPa, and has a thermal conductivity greater than 1.0 W/m-.degree. C., and a thickness of between about 0.08 mm and about 1.0 mm. The low compression modulus of the gel material protects the chips from the transmission of mechanical stresses thereto.