With the advent of heat assisted magnetic recording (HAMR) [1] the thermal transport properties of magnetic recording media have become a key performance characteristic. In particular it is important that lateral heat transport is minimised in order to heat only the localised bit area and conversely that vertical heat transport is optimised for fast cooling of the medium essential for the thermal stability of written bits. Magnetic media are multilayered and highly structured on the nanoscale rendering classical treatment of thermal transport inapplicable and the likelihood that the transport is dominated by interfaces and dimensions rather than bulk material properties. A technique for measuring thermal transport on the nanoscale is therefore highly desirable in the design of new magnetic media. In this study we explore the potential of scanning thermal microscopy (SThM) to resolve thermal transport on the nanoscale and use a multilayered, grain segregated conventional disk.