Heat is seriously ungood for CRT glass. It reduces the
strength of the glass which can lead to arcing through the glass.
Does the diellectric strength increase back to its original value on
cooling again? If so, then this is not really a problem if you happen to
heat a CRT part (pin, bit of the envelope) with a soldering iron while
working on the device.
I'd be much more worried about thermal stresses causing the glass to crack.
Prolonged arcing will hole the glass, thus venting the
destroying the tube. Magnetic deflection yokes need to be designed not
to run too hot, the glass needs to stay well below 100 degrees C. Above
120 deg C the glass has not much dielectric strength left.
As an aside., if oyu conenct a glass rod (just about any type of glass
will work( in series with a suitable load (an electric fire element, for
excample) across the mains, not a lot happens. The glass is a good
insulator at room temperature. But if you then heat the glass rod with a
bunshn burner or gas blowlamp, it'll start to conduct, and will in fact
glow. Often it 'runs away' and gets hot enough to melt.