There are two aspects to fluid thermometer making: the glassblowing and the calibrating
Thank you for posting this old Kodak fix article. I have the same mentioned Kodak Type 3 mercury thermometer that has had a split in it for the last year or so.
I fixed mine in like 10 seconds, doing this:
1 graduate with tap water - 50F.
1 graduate with 170F water.
What I found if I quickly ran it near the top in the 170F and then immediately over to the cool 50F water, the rapid rise/fall made the mercury split disappear magically.
Heating method is the only way to solve it. The only problem is the media used to heat it up.
If the thermometer is somewhere lower than 100degree Celcius, you can use boiling water to achieve it.
In case you have some high temp thermometer, you have to use different media to heat it up.
Glycerin (pure, 290'C) or cooking oil (i.e. olive oil, approx 250'C or higher, but it may has reached burning point) can do the work.
IF you have a thermometer higher than 300-350'C, you'll need special media to get that hot. Sorry I forgot the name of the oil (wax), if you need the name, let me know. I'll have to check it out.
Be aware of the cooling steps. The higher temp, the shorter reacting time to remove it from boiling oil.
You may try din-in (long time) & out (short time) to raise the temp gradually until "splited part" "unsplited".
ALSO, the higher temp, the longer, smoother cooling needed. You can also use dip-in (shorter time) - out(longer time) until it's lower than 100 degree'C. Fast cooling will cause craking.
Be slow to get to the top. They do not like overpressure.
That is why cooling should be an alternative method.