In　this　paper,　we　are　concerned　with　the　conservation　of　energy　criterion　of　the　weak　solutions　to　the　Navier–Stokes–Fourier　equations　on　the　torus　allowing　vacuum.　We　establish　the　energy　conservation　criteria　via　the　gradient　of　velocity　for　the　weak　solutions　of　this　system,　which　generalizes　the　corresponding　recent　energy　conservation　criteria　in　terms　of　the　velocity　obtained　by　Aoki　and　Iwabuchi　in　Aoki　and　Iwabuchi　(2022).　Moreover,　sufficient　conditions　for　weak　solutions　keeping　the　energy　balance　allowing　vacuum　are　shown　for　the　full　Navier–Stokes　equations.　©　2024