Hey scotty I got me a interesting situation. I have a 2007 Chevy Equinox LS with 101k miles in it that i bought used from a dealership. My heater a couple of weeks back stopped working and I was told that my thermostat and heater core needed to get replaced. So, I had my thermostat done a few days ago and I just got my heater core replaced yesterday. I noticed that when I'm on the highway my heater works fine, but when I'm in the city, the heat tends to cool down and heat back up again. I don't know if its my heater core or my thermostat thats faulty or can it be something else? P.S. I hope you and your family have an amazing holiday!
It sounds as if whoever did the job did not properly burp the cooling system of air and you're getting cold spots. I would take it back and tell them to properly evacuate the air out of the system.