When you say God died, are you meaning both Deity and humanity of Jesus, or just He physically died?Perhaps this might be a bit more nuanced than that. By analogy, God is Spirit. He cannot be seen (nor tempted). Jesus is God. Jesus was both seen and tempted. Was “God” tempted?
The Son was tempted through his human nature and only by that occasion. Notwithstanding, a person was tempted, lest a person did not fulfill all righteousness on our behalf. In the like manner, not just a human nature but an actual person died upon the cross, lest we aren’t redeemed (and only our natures are redeemed).
Excursus...It’s my understanding that William Lane Craig and J.P. Moreland do not think Christ has two wills, a human and divine will. But wouldn’t this imply our wills are not redeemed? As Oliver Crisp points out, they may save themselves from violating Chalcedon. Maybe. But as Crisp also observes, do they violate the 3rd Council of Constantinople? Should we affirm monothelitism? I should say not.