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.
That would seem likely since the glass was once melted in
order to make
the CRT. Whether continuous arcing damages the glass permanently or not
is another question. I would guess that the heat in itself does nothing
irreversible, but arcing does.
I found this in a text about types of glass and manufacturing procedures
for CRTs. It did not mention whether the damage was reversible or not.
Your observation about connecting a glass rod across the mains and
heating it certainly supports their warnings about reduced dielectric
strength.
On the other hand, I would suppose that severe localised heating could
cause the glass to crack due to local expansion creating excessive
stresses, so I would still be very careful with the soldering iron.
/Jonas