I am about to do my first all-grain batch. After (batch) sparging is it safe to drop the hydrometer right in or do I need to let the wort cool to a specific temperature first? I realize I will have to do a temperature correction to get the proper pre-boil reading, I am just wondering how hot is to hot for a hydrometer to withstand.
There's definitely a thermal shock issue, and you shouldn't place a hydrometer into any hot liquid … but I don't think that's what you're getting at.
I, too, imagine the hydrometer temperature correction factors will break down after some point, but I can't respond to where that point is; I'd not go past 90°F.
Before I got a refractometer, I would have a collection of ceramic mugs into which I would take pre-boil samples, letting them cool throughout the brewing process, and then taking the hydrometer measurements later in the day at the end of cleaning up, when the mash runnings/wort had had enough time to cool down.
The issue with the hydrometer is the weights inside of it. The weights will heat at a different rate than the glass and result in pressure against the glass. I lost my first hydrometer by rinsing it with water that was too cold. The suddenly cold glass shrank just enough to press against the warmer weight inside and the glass cracked. Even if I were to slowly raise the temperature, I still would not want to risk the physics of a mass of metal glued inside of a tight glass enclosure. If I knew my thermodynamics, I could give a more scientific explanation.
jsled also raises a good point about temperature correction. The hydrometer is calibrated at room temperature. The further you deviate from that mark, the less accurate your reading.
I have broken a Hydrometer by placing it in a too hot wort. The end cracked right around the weighted end - see @Bad Neighbor's answer. Once bitten, twice shy. Now, I always cool the wort in my hydrometer vessel by running under the cold tap, or submerging in a bowl of cool water, for a few minutes.
I try to get the temp down to around 25-30 °C (77-86 °F) and then do a small adjustment to the reading.