The amount of heat given off by the current in the rod when the potential difference applied to the ends of the rod is constant will equal, from Joule-Lenz's law,
Q = 0.24I²Rt.
It will obviously be greater, the lower the resistance R. Since asbestos slows down the giving up of heat to the surrounding atmosphere, the rod will be hotter inside the asbestos. But R for graphite falls as the temperature rises; therefore Q will be greater when the rod is covered with asbestos.