My husband and I were wondering if there is any way for him to temporarily adopt my children while there biological father is incarcerated?

Why does he want to temporarily adopt ? It isn't possible anyway. You are their legal guardian that is all that matters.

Tick

Nope. There is no such thing as temporary adoption.

The bio father would have to sign his rights over for an adoption,

And these are not puppies at the pound, you either adopt ( which is forever) or you don't.

But the main issue is not a silly picece of paper that adopts them, the question is, does he treat them and care for them as his own children. That is a sign of a real father.