2007 GMC Envoy thermostat

I have a GMC Envoy and recently had a newer motor put into it. two days
after the replacement, the "check engine" light came on. Of course, I called
the mechanic who replaced the engine and he said that the thermostat is
most likely good, seeing as that it is not overheating or running badly, but
that the sensors on the motor and thermostat may not necessarily be "in-
sync". I did not replace the thermostat yet, and we have had warmer
weather, so the light remained on As soon as the ambient temperature
dropped below say 40 degrees, the light went out. Again, the weather
warmed up and the light came back on. This morning, it was 31 degrees
outside and low and behold, the light is out again. I am just wondering if the
ambient temperature has any effect on the thermostat (thus the check
engine light)?