Yes that would certainly indicate the T Stat is bad and needs to be replaced.
These are notorious for that problem.
What has happened is that the T Stat is no longer making any contact internally therefore, no fan lol:-)
The best place to get that part is listed below (link).
Also I have included the phone # for your convenience.
I would call them to be sure they send the correct part, its always better to speak with a parts rep.
Tech Michael Here is your requested info:
Product support opening times: