My engine warning light is on, they serviced and said the only reason for this is an old thermometer outside of the engine itself and it is not an urgent fix.
This is not the thermometer inside the engine that works with the coolant.

So my question is....
What thermometer is this?
Is it important to change asap?
Why does something outside the engine cause the engine light to go on?

 

Could you get the codes read again and post the exact code number here? The only thing I can think of is the Engine Coolant Temperature Sensor. But having the exact code number will help us give you much better information. We will be waiting. Thanks.

 

There are sensors that detect the temperature outside the car, but all that information is shown on a display to benefit the user. It doesn't have anything to do with what the engine does, therefore it shouldn't give a Check Engine Light.

Automotive Temperature Sensors
^A bunch of other sensors that detect temperature.

 

First...Year, Make, Model & engine would be nice.

You have and intake air temperature sensor and quite a few engines use two coolant temperature sensors. One is used for the temperature gage/idiot light and the other is used for the emissions. The one for the emissions is used by the CPU to help determine how much fuel to deliver.

If the coolant sensor for the emissions is bad and makes the CPU think that it's colder than it actually is, it will run rick and wash the cylinder walls down leading to premature wear and fuel dilution of the engine oil.

So, yes...I would get it fixed, but I would also find another mechanic.