I remember your house now that you referenced it being an old ski shop. I think I made another long winded comment on something you wanted remodel.
If you have the make and model of the thermostat you installed I could look, it up and check out the wiring diagram and give you a better idea of how to go about trouble shooting.
But as I said I doubt very much a mouse has eaten through the wire and “cut” the circuit. I am a big believer in the problem-solving principle known as Occam’s razor (or Ockham’s razor).
Occam’s razor (or Ockham’s razor) is a principle from philosophy. Suppose there exist two explanations for an occurrence. In this case the simpler one is usually better. Another way of saying it is that the more assumptions you have to make, the more unlikely an explanation is. Occam’s razor applies especially in the philosophy of science, but also more generally.
With that in mind I have found that the most likely “simple” problem and fix is a loose wire connection somewhere. If wire nuts were used to splice there is a good chance that is where the problem is. I have run into this a number of times. Everything looks good when done, nuts are tight etc. the circuit works close everything up. A couple of days, weeks later no power. A wire came loose in the “splice nut”. It is more likely to happen in multi-wire splices. If there wires are secured with a screw connection make sure they are really tight.
Wires on high demand circuits can and do get somewhat hot. So they expand and contract and work themselves loose. I have experienced all the above. On my work and that of others, the ones that are supposed to be licensed pros. I have found more problems on the later.
So, I would go back and check all of the connections to start with. Having and knowing how to use a Multi-tester makes things easier and faster to figure out.
I installed these last year. Very easy to install and program. No batteries needed they are powered off of the line voltage.
http://www.homedepot.com/p/Honeywell-5-2-Day-Baseboard-Programmable-Thermostat-RLV4305A/100566648
I checked out these which replace the simple thermostat mounted on the baseboard. But considering that baseboard heat works by convection, the heat rising and drawing the cool air in from the floor I wasn’t too sure how accurate they could be. But they are programmable and don’t require running any wires through the wall. They don’t have as many “event” settings as the one above.
http://www.homedepot.com/p/Cadet-Smart-Base-240-Volt-5-1-1-Programmable-4-Events-Day-Baseboard-Thermostat-in-White-SBFT2W/100495411
Yup, I know what you mean about hearing the little buggers behind the walls. Grew up in and have lived in lots of old houses. You get used to it. Out of sight out mind. I really hate squirrels in the attic above my bedroom. Easier to get rid of then mice in the walls.
I had a cabin in the foot hills of Colorado that I built out of recycled materials. Used old cedar fence boards for siding. The first spring I was spending some quality time there I was awoken every morning with a rapping on the outside wall. I’d get up go out and look, nothing. This happened for several days. Really annoying. One day I saw a bird fly off and settle in a nearby tree. Turned out to be a Woodpecker trying to make a nest in the soft wood siding. Wasn’t easy to persuade him/her to go somewhere else.
“I’ve learned mice love certain kinds of plastics”
So do wildlife. The first time I went to do some climbing in the Canadian Rockies and pulled into the trail head parking lot there was chicken wire laying around. We were thinking this is kind of strange for people to be leaving “garbage” like that. We were in a pretty remote area. While checking out the trail head sign there was a “note” about the chicken wire. Turns out the local wildlife especially the Canadian Marmot which are quite large and friendly like to chew on the rubber break lines that connect the metal lines to the break calipers. The note instructed people to wrap the chicken wire around their break lines. Sure glad we read that note because it would have been a BIG hassle to come out the mountains a couple of weeks later and find out our car had no breaks. We were WAY off the main road and a LONG way to the nearest parts store.