I strongly suspect if I had called for service, I'd be told I needed a new furnace, even though this one is less than a decade old.
If it was on the flue, then it's a symptom of a drafting problem when they fail. Basically the thing should rarely ever click, but if the flu isn't drafting well, then the snap disk will get triggered frequently. You'll never notice anything wrong because the heat still works fine.
Then the thing fails and you fix it, but you only fixed a symptom and not the problem.
Even so, I still think it's better to get in there and figure stuff like that out than to avoid it. "just let the professional do it and do whatever they suggest" only works if you have some way of finding a guy who is both knowledgeable and honest. Yeah there are obviously risks like being unaware of invisible unsuspected things like above, but life is risk regardless.
It took an extended run to get the house back up to temperature, but it had no problem with a correctly functioning switch.
This results in higher efficiency and better steady state comfort as the heat is on for always 18+ hours and often 22+ hours per day. It’s hard to say with confidence on the precision, but it seems like this is saving 8-10% in gas (in therms) vs last year when I had a constant flow temp (that I’d adjust manually every so often to try to match but where I’d have to leave it “too high” or risk a cold house on the coldest days).
The exhaust temps in the stack reach steady-state far before even a 30 minute run would be finished.
A high limit trip will generally cycle the furnace off for a time period. Somewhere between 3-5 off cycles will result in lockout and the furnace will stay off. The control for this is more likely to reside in the furnace board vs an aftermarket ui.
This indicates you have a problem with temperature rise across the heat exchanger, probably from inadequate airflow. Your ducts may be sized too small/furnace too large, fan speed set too low, plugged filter, etc. You may be able to mitigate the problem by increasing fan speed, limiting heat by using stage 1 only, putting in less restrictive filter, add additional cold air return, etc.
Usually a failed limit switch means cycling and a bigger problem with airflow. However I have seen a high temperature limit switch fail without cycling - fell apart with age (40 year old furnace).