When I got divorced in 1975, I had one of those tiny dorm sized refrigerators in a $100/month rent house. If I put a warm container of food in that thing, it would have defrosted it!
The most relevant factor to putting warm food in the fridge, is the size of the cooling plant. It could lower the box temperature enough to become a hazard for other foods inside the box......milk especially.
It can take 12 hours to properly calibrate a fridge. It would take a while before you really knew how well it worked.
For big family parties at the house. I'll take my 80qt cooler and put 3 bags of ice in it and put my left overs in there for first night. It'll drop temp quick on items