If a thermostat is bad, it can seem like its running normal but get poor fuel economy or even run a little poorly due to running too rich.
Basically, a thermostat is designed to open/close at certain coolant temperatures depending on the specifications needed for that vehicle (usually around ~180-195*). If it sticks open, for instance- the coolant will not get hot enough and the vehicle will not reach normal operating temperature, thereby staying in what's called "open loop" (warm up mode so to speak) where the vehicles computers do use the sensors to run the car, but not effectively. It runs the car through a series of programmed defaults "hoping" to hit that magic 14.6:1 air/fuel ratio. Due to the lack of communication from the below listed sensors, it never really knows.
In
closed loop the computer takes information in from the MAF (Mass Air Flow) sensor, oxygen sensors, knock sensors, IAT (intake air temp) sensors, coolant temp sensors etc.... to get the information it needs to run clean and efficient. The reason you have open loop is the oxygen sensors won't work until they are at least 600 degrees farenhiet, therefore it has to run on programmed settings until they warm up. As stated above, the oxygen sensors work hand in hand with IAT, ECT and MAF sensors.
This all about as clear as mud? I'm sure I could have explained it better, that that's the gist anyway.
Here's a good article to read that keeps it reletively easy to understand. I know it applies to Fords, but you get the point.
http://www.musclemustangfastfords.com/tech/0607mmfp_ford_efi_system_tuning/fuel_control.html