Ect temperature fluctuation

[Joel2013]

So recently my 2013 Equinox lt 2.4 ecotec. Began to show codes p0118 and p0119. So I just went ahead and replaced the thermostat and the ect sensor. This took care of the codes and all the issues. However, less than 20 miles after doing this the same problem of the temp gauge and a/c not working began to happen along with the same codes. So I hooked up a scan tool and the ect temp will read between 140-150 at operating temps, but as soon the car is shut off the temp reads between 190-205 depending on whatever the actual temp is at the time. So my question is this an issue of a short in the circuit or an issue with the ecm? Or is it something simpler that I'm overlooking? I'm trying to avoid taking it to a mechanic just so I can learn to be more hands on since I have a little extra free time right now. Thank you.