Hephaestus is the Olympian god of fire and technology. Like the two other gods who carry out Prometheus's punishment, we don't learn too much about him—but we do get the sense that he's not a particularly powerful god.
Even though Hephaestus claims that he doesn't want to imprison his kinsman Prometheus, there's not much force behind the words. When Power starts to menace him, he changes his mind pretty quickly. Sure, he might complain that he "hate[s] [his] craft skills" (46), but he doesn't exactly try to stop the punishment from going forward.
Hephaestus also says something interesting: he says that "the mind of Zeus is implacable—and everyone is harsh when new to power" (35). This sounds a lot like an excuse for Zeus's nastiness, and it also helps us see the war between the Titans and the Olympians as a real conflict. After all, what do you do when you win a war? You punish the traitors—hard enough to make an example.