Wort temp during high krausen

What is the temperature difference between the wort temp inside a brew vessel during high krausen and the environment temp outside (say, the refrigerator). I've heard 3 degrees F at peak fermentation but can't find any hard data confirming this. Controlling the refrigerator temperature with a probe and thermowell would likely yield wild temperature swings without use of a PID controller, so for the moment I'm planning on simply adjusting the air temp down a few degrees to compensate for the difference. Primitive, I know, but economics necessitates this for the moment.

I've had 6 degrees more inside the fermenter than outside during high krausen. But it's not always the same.

There's too many other factors to give a definitive answer. I ferment in a basement where it's pretty consistently 60*. The earth around the basement, plus the concrete floor makes for a huge heat sink. I usually use a combination of blankets and heating pads to regulate my fermentor's temp. I really have to check it twice a day if I want consistency. I start by pitching around 62 and just wrapping a blanket around it. Then when fermentation starts it usually jumps up to about 65. At this point I might turn on the heating pad, but it can rapidly raise the temp if I'm not careful. Then as fermentation winds down I like to boost to 70-74 for cleanup, and this usually requires a tight wrap from the blanket and the heating pad set to high.

People frequently say "fermentor temp is usually 8 degrees above ambient" but that's too broad. You have to get a fermometer on the side of your carboy. Don't be like one of these people who guess and would basically rather not know what their temp is so they can assume it's where it should be.

I use an aquarium heater in a bucket of water that the carboy sits in to control fermentation temp. I have compared the temperature of the water to the internal temperature of the wort throughout fermentation and I get a 3-4 degree difference when fermenation is just picking up and ramping down, and a 6-8 degree difference at high krausen.

My plan to build a fermentation chamber that is controlled by the internal temperature of the fermenting wort (not the ambient temperature of the fermentation chamber) as this is the only way to ensure proper fermentation temps.