1985 Toyota Corolla Bogging down while in gear

Dear 2 Car Pros, thank you for your excellent site. It has been of great help to me until now. My wife and I just bought a 1985 Toyota Corrolla wagon, 107,000, 1.6l, with an automatic trans. The engine idles fine and revs freely while in park or neutral. The problem is once I put it in drive and try to accelerate, it is totally bogged down through all three gears. Only by flooring it will it accelerate strongly in its passing gear. The bogging problem makes it really hard to drive around town let alone get up to 50 mph. Otherwise, the auto trans shifts smoothly through each gear and back down when coming to a stop. One other thing is that the thermostat is not working. It may be broken or stuck open as the engine will not come up to or stay at operating temperature. It has been quite cold out here. The fluid and filter were just changed by the dealer before we took it. I am unsure where to begin, do you have any suggestions?
Thank you in advance,
Kevin Bishop