My first thought is just that there is something wrong with the thermostat since that is exactly what these symptoms point to. Strange things happen during working on cars. Was the cooling system flushed when the thermostat was replaced/heater core flushed? For a manual flushing the thermostat is removed. Perhaps someone literally just forgot to put it back in. Another possibility is that the new thermostat was bad off the shelf. It happens.
If the car’s temp gauge was going to normal I’d say to keep looking at a heater core problem. But since the temp gauge is staying low this really just points to a stuck open thermostat.