Engine light is still on?

It must be the A/C termostat that needs replacing. It is located on the evaporator which is in the heater/A/C box on the passenger side of the car under the dash behind/near the blower motor. It looks like a small radiator and will have some insulation around it. The temperature sensor will bw attached then have a copper tube that ends with the temp sensor up against the evaporator. The whole assembly needs to be replaced. Four Seansons is the prominent aftermerket A/C parts maker and you can find the part on rockauto. Com or usautoparts. Com or use the search engine on this site to locate A/C parts dealers.
If I misundertand the question and you are talking about the coolant temperature sensor. If you have a temperature gauge in your car, you will have two temp sensors for the coolant. They are located in the same area near the thermostat usually. You will find one with two electrical wires and the other has one. Replace the one you have not replaced yet and see if that keeps the check light from coming back on.
The A/C may be un-related in this case and need to be diagnosed sperately.

Replace the sensor first and see what happens.
The A/C could be a whole other issue.
So, if the trouble light comes on have the trouble codes pulled. Any Auto Zone or Advance Auto will do this for free.
The thermostat that I am refering to is the temperature sensor for the A/C. It senses the temperature at the cooling exchanger. It will come up in the trouble code if it is bad.