Grain-to-grain Curie temperature (Tc) variation in the media reduces signal-to-noise ratio due to its contribution in transition jitter noise, especially when average grain size is pushing down to increase the area storage capacity. A thermally insulating magnetic grain boundary may suppress such grain-to-grain Tc variation, especially at small grain size. Here we present an experimental study on the effect of adding thermally-insulating magnetic oxide, in particular BaFexOy, as part of the grain boundary materials in granular FePt-C HAMR media. It is found that the BaFexOy is chemically inert to FePt and the chemical ordering of FePt-BaFexOy-C media are similar to that of FePt-C meida. By tuning the volume fraction of BaFexOy and C, well-separated FePt grains (average grain size = 6.8 nm) surrounded by BaFexOy shell with perpendicular Hc above 35 kOe can be obtained. Transmission electron microscopy study with chemical analysis shows that the magnetic oxide appears to be crystalline and surround the FePt grains with immediate full enclosure. Magnetic measurements indicate an effective increase of magnetic grain size at temperatures below FePt Curie temperature. Pulsed laser pump-probe measurement indicates a measurable reduction of Curie temperature variation for the FePt-BaFexOy-C media with carefully comparison with the reference FePt-C media.