Grain-to-grain Curie temperature (Tc) variation in media reduces the signal-to-noise ratio due to its contribution to the transition jitter noise, especially when the average grain size is decreased to increase the area storage capacity. Thermally insulating magnetic grain boundaries may suppress such grain-to-grain Tc variation, especially at small grain sizes. In this paper, we discuss the effect of adding a thermally insulating magnetic oxide, in particular, BaFexOy, to the grain boundaries of granular FePt-C heat-assisted magnetic recording media. It is found that BaFexOy is chemically inert with respect to FePt and the chemical ordering of FePt-BaFexOy-C media is similar to that of FePt-C media. By tuning the volume fraction of BaFexOy and C, well-separated FePt grains (average grain size = 6.8 nm) surrounded by BaFexOy shells enable the attainment of perpendicular Hc greater than 35 kOe. Chemical mapping by transition electron microscopy shows that the magnetic oxide appears to be crystalline and completely surrounds the FePt grains. Temperature-dependent magnetization measurements indicate an effective increase in the magnetic grain size at temperatures below the FePt Curie temperature. The pulsed laser pump-probe measurement indicates a measurable reduction of the Curie temperature variation for the FePt-BaFexOy-C media compared to the reference FePt-C media.