Got a P0116 code on a 2006 Toyota corolla ?

I would take a good look at the coolant temp sensor and the coolant level.
The code sets when the temp change between start up and the vehicle being driven is only 5.4 deg F or less.
Even if the t-stat was stuck all the way open the temp change should be more than that.

This is not a hard repair and you can do it your self with common tools in about 30 min. Inspect the wire leads to the engine coolant temperature sensor (ECT), look for any damages like corrosion or a break in the wires. If the wires look good then replace the ECT and the thermostat, standard thermostat 80"C to 84"C (176"F to 186"F)
If there is an Auto Zone around your area or Parts Source, you can pick up the two items I mentioned and they can give you the step by step instructions to getting the job done, Note: do not over tighten the bolt to the thermostat housing, since the manifold will be aluminum and you don't want to strip the manifold where the bolt goes in to. Good luck and keep em posted for any other questions.