Cooling down

The danger zone is 40° to 140°, with the most dangerous temps being in the 60° to 80° range. Serve Safe says you have 4 hours before the temp needs to be 40° or below. Your situation sounds iffy to me.

One thing to remember is that house hold refrigerators are designed to keep things cold, not cool them down, hence your warm fridge. I always use an ice and water bath with an ice bag on top to cool the meat down to cold before fridging.

Hopefully others will chime in with more info.

Your food is fine. Look up two stage cooling method. You can take whatever the health department, usda, serv safe and all the other place out there and add a little time, there stuff is extreme to ensure no problems. There is a lot more room for error then you might believe.

FWIW

When I cook extra butts, briskets, etc--I pull/chop/whatever and put in aluminum pans. Each pan is loaded shallow, no more than 1/2 full.
These are cooled for a bit to near room temp and then into the freezer for a couple of hours.
Quick chill and does not have enough residual heat to drive the freezer temp up much, if any.
Then vacusuck or whatever I plan for storage.

Works for me.

Your meat should be just fine the way the timing worked out.

TIM