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Coolant temp sensor.

More specifically, it's the temp sensor used by the ECU.
The gauge has a separate sensor located on the block.

so in other words it's very important lol what would happen if this were to break off entirely?

It's a 25 dollar part at autozone.. just replace it. Don't forget to bleed your cooling system after.

As clokker said, that is the sensor used by the ecu to determine how warm the engine is.. which in turn directly affects how your car will start and run because of the difference in fuel requirements.

I've changed this sensor out before..and If you have good access to it and are Quick..(not like on Meth or anything.,lol..just not fumble nuts slow!)..you can pop it out and exchange it for new and lose about an ounce or two of coolant.

Ya.it's important..anything to do with the ECU and Temp is crucial as it alters fuel maps too..so that thing needs to be in good working order and connected up so that the ECU can read the temp of the engine.

ECU will keep the car rich, thus poor fuel economy, smell, even backfires. And that's if the sensor doesnt make continuity with the pins sticking out of it. I had all kinds of fun when mine had a similiar issue

important enough that how you have it pictured it is most definitely non functional.