In the interior of a hot-Jupiter, core erosion takes place at a temperature of roughly 10,000 K or more. The high surface temperature on a hot-Jupiter induces the conditions needed for core erosion to occur. Erosion frees the deuterium needed to react with the non-eroded part of the core. This process can continue for billions of years, supplying the deuterium needed to sustain DD fusion and maintain the core region at ~10,000 K. The energy produced from DD fusion can keep the hot-Jupiter inflated, and in some causes, even over-inflating the hot-Jupiter.
Ouyed & Jaikumar (2015), “Nuclear Fusion in the Deuterated cores of inflated hot Jupiters”, arXiv:1506.03793 [astro-ph.EP