We have no idea what happened with the Heart of Sabik after the Preatorium. That said, the last person we do know of in the area with the Heart of Sabik is Gaius himself. And he has been somehow killing Ascians without being able to manipulate aether himself. Given that the Heart of Sabik can absorb aether like no one's business, its been speculated in some areas of the fandom that Gaius has the Heart of Sabik still and is using it to kill Ascians.

I find it a lot more likely that it's the Weapons being moved that Gaius is talking about in that scene, if only because the Weapons are huge and Gaius and Estinean didn't have a lot of time to do anything while fleeing from the Praetorian Guard. The Heart of Sabik is... pretty small and could conceivably be just about anywhere. I have a hard time seeing Gaius go looking for after Varis died while in the middle of being hunted down. It's a lot more believable that he fled through the place he knew the Weapons were and noticed they were all gone.