You don't need an extra thermometer (although I do recommend an IR temperature gun, because it's fun and you can use it for all kinds of stuff around the house).
Do the dollar bill test on your door gasket every year. Close a bill in the door, try to pull it out. Should be very difficult unless you have a graphite (black) gasket. Go all the way around the door testing. If there is an issue, adjust the door. If the door can't be adjusted any more, replace the gasket.
In summary:
1) Follow all the directions in the manual
2) Check your door gasket at least yearly
3) Keep an eye out, but don't worry too much about the rest.
For further overfiring tips, read this thread from the top, but user error and door gaskets are the common ones.
Regarding the overfire bholler was talking about- check me if I'm wrong here, but that was the first time that we have heard of that happening due to excessive draft. It's not even usual amongst people who have tall flues.
Think of it like a car. Can it catch fire? Yes. Has that happened? Yes. Is it likely? No. Can I prevent it with inspection, attention, and maintenance? Yes.
Bonus: it's a lot easier to keep an eye on your stove than it is to inspect your whole fuel system regularly.
Double bonus: Used the car analogy to provoke Ashful into telling a car fire story, which I am hoping he has one of. Hopefully there are JATO bottles involved.