As the magnetic data storage industry continues to pursue aggressive miniaturization of sensors and write elements in thin-film recording heads, it faces serious thermal management challenges. The present work develops theoretical models of heat conduction and power dissipation in current-in-plane and current-perpendicular-to-plane sensors to highlight key physics and help examine the influence of various parameters. Fundamental physics of heat conduction in thin films and across interfaces is discussed to facilitate systematic exploration of novel high thermal conductivity materials and methods to minimize the thermal interface resistance. Experimental techniques for thermal characterization of recording heads and constituent thin films are also presented.