TBH, I'd never heard of "temporal punishment". And, when I googled the term, it only brought up Catholic sites. I don't see it as something that is agreed upon across all of Christianity. Unless there's a different, non-Catholic term, that is used outside Catholicism. If that's the case, then I'd bet we'd disagree that they mean the same thing.temporal punishment (a doctrine pretty much agreed upon across the spectrum of orthodox Christianity).
I guess I see a difference between suffering the consequences of our sinful nature, while still in the flesh, and suffering the consequences of our sinful nature, after we die, and our sinful nature is gone. I don't see that those in Christ will have any punishment for sins after we die, and leave our sinful nature behind. I guess I don't equate purgatory, and the bema seat. One is punishment, and one isn't. At least that's how I understand it. Perhaps I'm missing something?