"It's good that you are using a proven circuit configuration. This helps narrow down the possibilities. It would be helpful if you stated the temperature readings you are getting over time. Example, at power on, one second…"
I attached the datasheet because I am not sure if you have it. Read it over if you haven't already.
It is probably measuring the temperature correctly so you have to figure out what could be making the temperature go up. It…"
"If you get lights and blocks then the LCD is working and not getting any data. It looks like the JHD uses the HD44780 chipset, so it should work with the LiquidCrystal library. I'd check your wiring, or redo it from scratch.…"