A read head structure is disclosed with a dual piece heat sink layer having a front piece formed over a front portion of a dynamic flying height (DFH) element and a back piece above a back portion of the DFH element. A first (S1) shield is formed on the front piece and between the front piece and air bearing surface (ABS). Front and back pieces are separated by an insulator gap. The front piece is used to help control read gap protrusion. As a result, a bottom portion of the S1 shield protrudes to a greater extent than a top portion adjacent to the sensor thereby protecting the sensor from unwanted contact with the magnetic media. The dual piece heat sink layer also enables an improved Figure of Merit in terms of temperature rise in the reader per unit of actuation (nm) delivered by the DFH element.