To be a picky metallurgist, it can actually be beneficial to cool the parts, then re-heat and quench.
As a rule of thumb, when reheating it takes about 5 minutes at heat to burn out enough of the surface carbon to be a problem.
Me, I'd just dump the whole contents of the pack into water, holding the pack near the water to minimize exposure to air. If you don't like the mess, well . . .
In the early 1970's I recall a video promoting the advantages of vacuum carburizing. The advantage they were promoting was Kindness to the Heat Treater.
Showed the heat treater at Smith & Wesson dumping a pack full of carbon, hammers & triggers into the water quench. Messy, messy, messy. But (at that time) S&W did make good stuff.