AIR FILTER MONITOR
 

What would cause the air filter monitor to get so hot that it melts and comes apart?2004 6.0

One possibility is your engine compartment is getting hot; if that's the case, I would suspect the engine is the source? If your not getting a high temperature reading on your dash, the sensor could be bad.

Is the engine blowing coolant out the degas bottle?

I just leave mine unplugged but I also clean my filter on a somewhat regular basis. I would think it would have to be a set of bad contacts in it, it is just a switch.

The temp. gauges have not shown any have temps.It's not blowing coolant,but it is blowing bubbles in a test container.Most likely ahead gasket,the egr has been deleted.

I'm going to make a wild guess and say that your temps are not showing high because the temp sensor does not have fluid contacting it. A temp sensor will only show the real temperature if fluid is contacting it.
So, my guess is your head gaskets are blown and you have gas, either steam or exhaust, in your cooling system.
The air filter monitor is melted because your engine compartment is indeed hot...very hot.