Unfortunately, it wasn't the thermostat. The mechanic gave the car a thorough going over and said that the fuel-pump wiring had shorted out, and there had actually been a small fire in the car (explaining the electrical burning smell we'd smelt). The wiring would need to be replaced, and so would the fuel-pump. Total cost was roughly $700, plus tax.
This level of investment didn't make sense, given that Freddy in all probability had no more than a year left to it. So, we gave it an honourable death, and told the mechanic to clear out everything of value (a new CD system for one) and take the car to the scrap yard.
It will be some time before we can think of having another car. Fortunately, this won't be so bad. Erin and I can carpool to work, and the local transit is excellent and getting better. However, Kitchener is a city that has been built around the car, and we'll be missing Freddy, even if we are likely to save at least $150 per month in gas, parking and insurance as a result of his demise.