LCD showing weird characters when using two 1-wire temperature sensors
After some more searching I have found Arduino forum topic LCD text corrupts after Arduino runs for length of time. I have followed this advice:


  In particular, try running the LCD ground wire directly to a ground pin on the Arduino (not to the breadboard) and keep it short.


This seemed to solve the issue, therefore it was likely some kind of interference on the ground wiring. (Before this, the ground to the LCD went trought the breadboard power bus).