I saw a sensor was broken today. It's located right under the air intake. It looks to be a Coolant Temperature Sensor.

A friend said it was for the Auto trans and the 5 speeds don't have this sensor.

Anyone familiar with this sensor? Will the car run better when I replace it?

 

Yes, it will run better, specifically in how it shifts.
I am surprised you aren't getting some tranny Faults.

 

Ya, no check engine lights.

My boost sensors vacuum hose in the back right of the engine compartment was split and the car was sputtering and not wanting to run. Even that didn't trigger a check engine light.

Wonder why.....