This disclosure relates to a multi-piece shield comprising a fence, a lid, and an insert. The lid attaches to the fence, which is attached to the circuit board. The lid is a relatively thick, flexible material for supporting the insert. The lid has a recess so that the insert can be recessed into the lid to position the insert closer to the circuit for enhanced heat absorption. The insert is made of a thicker heat absorbing material than the lid, again to facilitate heat absorption. The insert can be press-fit into the recess of the lid. The lid can have a dovetail configuration to retain the insert in the lid.