Mine is shot, and I run it during the spring/summer/early fall with the flaps open. I just let it warm up for a minute or two longer than usual. I haven't had any trouble yet, but a new t-stat is on my "eventually" list
The design is such that if the cable or t-stat fails, the flaps flip into the best position for optimal cooling at all times (I don't remember which it is, 'open' or 'closed')