I'm having the same problem! I have an '05 Fleetwood providence and have two spare t-stats, the same type as you show. For the past 5 years, I have been switching stats, when I see the "00" show up, or the stat, simply freezes up. I have been unplugging the existing one and plugging in a spare. I read another post by Pat Geddes, that spoke of the same problem. He finally found that one could order an electronic part, from Fleetwood (Choke Filter, #355469), and the cost was only $20.00. He said that solved the electronic interference problem, usually a flourescent ceiling light. I plan to do just that, when my Providence gets out of the shop, at LazyDays, in Tampa. If you are interested, the Fleetwood number is 800-322-8216.
Pat's post is "Heat/AC Thermostat Reads 00". Do a search of previous posts, if you want to read what he had to say.
Roland & Jerri, with Maggie & Mollie, our Pups; '05 Fleetwood Providence, 39' DP; '08 Saturn. "The difference between genius and stupidity is genius has it's limits" (Einstein)