Tubes, some of them, will have a coating on some of its metalelements inside
the glass envelope... This has to evaporate, burn of, by the heat...
That's the burn in for ya!!!
Not all tubes are manufactured this way. Or will need this.
So, are there pointers to this? Not really, you'll have to consult the manufacturing remarks ands so on.
If we look at the metallurgical side of things... as long a tube element never reaches the temperature
of "Eutectic..." of that specific metal, or coating, no burn in will apply...
Wikipedia on eutectic:
"When a non-eutectic alloy freezes, one component of the alloy crystallizes at one temperature and the other at a different temperature. With a eutectic alloy, the mixture freezes as one at a single temperature. A eutectic alloy therefore has a sharp melting point, and a non-eutectic alloy exhibits a plastic melting range"
Some of the coatings actually will evaporate, like water on a hot day...
The tubes envelope will become discoloured after some time of use.
Are there heat thresholds that a tube need to reach before the process will start?
hm...
Aluminum (that's aluminuminum for the Bush fans out there...

) will actually change shape in room temperature by pressure alone... meaning the molecules will "float" to a new equilibrium.
All metal elements wish to reach this state of crystalline or non-crystalline grid formation...
So during a heatingprocess, say turning your amp on, there may be going on some changes EVERY time
a given tube heats up...
It will then slowly reach a metal or shape equilibrium on a molecular level...
then you have a reverse process as it cools down.
All of this will depend on the materials used, what level of vacuum is inside the Tube (Torr), the construction, what type, is it gasfilled? ... yup! That's a quick lowdown on the break in of tubes.
Imperial