Packaging

Can we package the dumplings that is steamed before it is frozen and before its internal temperature reaches 41 degrees Fahrenheit?

Not enough information. But the short answer is no. 

Not enough information. But the short answer is no. 

So, we are a dumpling manufacturing company. And what we do is, we steam the dumplings and then we cool it for approximately 20 to 30 minutes and then we package it. The temperature of the dumpling after cooling only reaches 60-75 degrees Fahrenheit. So, is it fine to package the dumplings when it is at those temperatures? Or do we need to freeze the dumplings before packaging?

You need to perform destruction testing in all scenarios, look at the data and then decide  (by that I mean probe the centre of multiple dumplings in and out of packaging at the same intervals)

They may rise in temperature during cooling if already packaged

The #s will not lie