Hopefully, the topic of this thread is dealt with, and it wandering off subject is of no consequence?
The subject of "temperature" and popping expensive bits of kit into hot liquid has presumably been dissuaded? Now temperature and hydrometers. First, what is it we are trying to measure ... "Specific Gravity" or "S.G." or "Relative Density": I'll get a small jam-jar. It weighs 107.79g. Filled with tap water it weighs 211.11g. The water it contains weighs 103.32g. That's 3.644oz; I switch from grams so the "S.G." (which is a ratio and has no units) won't get confused with the similar looking g/ml which density is measured in. This is for real! But a jam-jar isn't a scientific instrument, so the rest is calculated (this is for illustrative purposes).
The jam-jar is emptied, filled with wort, and weighed again. The water has been sitting about in the same room as the wort so is the same temperature. The sample of wort weighs 3.779oz.
So: 3.779 / 3.644 = 1.037
The wort has a specific gravity of 1.037. At a temperature of ... who cares! It won't be making enough difference to register.
And water: Just divide the first result with itself ... 3.644 / 3.644 ... which is of course ONE! At a temperature of ... you've guessed it; "who cares"!
Now it just so happens we can get a device called a "hydrometer" that can be calibrated to measure S.G. Because we don't want to measure water that's been hanging around the same room as the wort, nor do we want to do the complicated division, so we'll assume the water has been measured at 20°C (it's a fixed "constant" at a set temperature) and the wort sample is also at 20°C. If the wort isn't at 20°C, we'll need a table to adjust the reading, and also take into account the 20°C water reference: Complicated! Lucky we've got tables.
The tables are derived from "empirical" data (the result of experiment) not mathematical formula. Any mathematical formula used by computer calculators will generally also be based on empirical data (immensely complicated "polynomials").
Now it just so happens we also can get another device called a refractometer. It can also be adapted to read S.G. But it's not only temperature that needs accounting for, but there's also the composition of different substances in the water ... and that includes the different sugars (like sucrose, maltose, malt-dextrins, etc., etc.), oh aye, and chuck some alcohol in too? Now that is complicated!
I'd be sorry for the condescending tone, except I'm not! I got fed up with having been marginalised for not using a hydrometer and will get my own back having realised I was right all along.