I don't think so. First the amount of smoke that can be produced from a small piece of burning plastic is huge. I saw an MCC room about 20' x 30' with a 10' ceiling filled completely with some of the darkest black smoke I have ever scene, down to a level about 4' above the floor. The plastic that was burning was part of a 1500 hp DC drive and was smaller than the thermostat in this thread.
As far as the damage to the baseboard, plastic often just smolders giving off a lot of smoke, but not a lot of heat. It takes a significant amount of heat to start the baseboard on fire.
I am sure the firefighters looked close enough to see that the smoke did not originate behind the baseboard. Something that can be done very easily if you are on scene, not so easy from a picture.