That's a neat way to do it without opening the device but it might be easier just to crack it open, find the chip and look for communications to either the LCD or even better, an LCD driver chip. Translate using an arduino whatever communication, either SPI or straight GPIO, coming from the main chip into whatever you need. This OCR looks fast to prototype but it's added computing resources and added cost (a webcam versus a $1 chip).
His way is a lot safer. It's never a "$1" chip, you also need a power supply for that chip, breadboard (or dev kit) which puts price into cheapo webcam range.
On top of that, breaking out to LCD pins or their drivers is not easy. They're often very fine-pitch pins, if they have pins at all, some can be QFNP packages making it even harder to get to the pins.
There's a big risk of just straight-up breaking the thermometer doing this, so if you attempt it, it's best to buy a backup.
A lot of these small LCDs interface with a zebra pad, hitting contacts on the LCD glass and some gold or carbon-coated conductors on the PCB. Gold conductors are easy, carbon-coated conductors are okay but can be annoying, but the pitch generally narrow for these, as you've mentioned.
