I had a similar failure with my hot water boiler, where an older solid state control failed such that when the circulator would kick on the burner would shut off. This allowed it to limp along heating, until a day when it was too cold out and I realized it wasn't keeping up.
re: libre software, my point isn't really about being able to audit the code, but rather about having a cross-device software-maintainer-maintained codebase that users choose to use.
FWIW another, probably better, way to mitigate this particular external temperature sensor failure mode would be a second larger control loop. When the indoor temperature is more than a few degrees below the setpoint (not as a result of a scheduled change), the furnace should be less-efficiently creating a larger amount of heat to get back up to the setpoint quicker. Which is funnily enough how people think most thermostats work when they ineffectively turn it up higher to get things warmer faster.