The present disclosure generally relates to data storage devices, and more specifically, to a magnetic media drive employing a magnetic read head. The magnetic read head includes an antiferromagnetic layer recessed from the MFS, a reference layer disposed over the antiferromagnetic layer, a free layer disposed over the reference layer, and a thermally conductive structure disposed over the reference layer. The thermally conductive structure is recessed from the MFS. The thermally conductive structure includes a first portion and a second portion. The first portion of the thermally conductive structure extends from the second portion of the thermally conductive structure towards the MFS. The first portion of the thermally conductive structure is aligned with the free layer in a stripe height direction. With the thermally conductive structure, thermal stabilization of the read head is achieved.