I live in an older home that is 15 feet from the light rail tracks. Last winter the furnace kept shorting out (an older furnace and replacing not an option) there was a wire that would loose contact with the metal plate and we would have to manually shift it around to get the furnace to switch on, finally at the end of winter the wire "blew" it was fried and now well we have no heat. I would like to have it fixed before winter comes again.

Now here is why I mentioned the light rail. I'm pretty sure that the reason the system has shorted out is when the train goes by the house will vibrate (house was built in 1884).

Is it possible to replace the thermostat that is "in" the furnace fairly easily? And can we find a way to keep it from happening again?

What kind of furnace do you have that has a thermostat in the furnace itself?