Hi Chris
"The bit was very securely tightened" = Can't be
The collet nut will not heat up more than the other steel around it.
That's the only way it would come free, it's like when you use a drill press,the chuck has 3 holes in the chuck to tighten it up on the bit most people think it's made so it makes it handy to lock the bit in place, Not true the chuck is made in 3 parts (jaws) that hold the bit and it should be tighten in all 3 holes, now when it comes to router chucks they have one split in the chuck collet the norm and a morse taper and all it takes is one good turn to lock it down all the way.
Bj
