Engines can actually overhead if the fuel/oxygen mixture runs too lean. If it runs lean the engine heats up real bad as does the catalytic converter. In some cases the catalytic converter gets fried. The heat on the converter is intense, in some situations the heat can be felt through the floorboards. Once the converter is damaged, your exhaust will start smelling like rotten eggs.
A bad O2 sensor can make the mixture run too lean or rich. But don't simply replace it just yet because those sensors are expensive and can run upwards of $300 by itself. On some cars there are two o2 sensors. One on the exhaust manifold and another one underneath on the exhaust pipe.
I've heard of PCM powertrain control modules going bad. But I'm not sure if that would cause this.
Your taurus uses digital technology to get by. Mechanical and digital co-exist.
Check to find out if there are engine codes. Even if the check engine light is off, there is a possibility that the dashboard bulb for the warning light has burned out.