Hello and welcome to JustAnswer!
Why do you think the thermostat is stuck open?
Where did you check the coolant level?
So the problems happened as a result of replacing the headgasket? It wasn't overheating or running cold, and had heat before the headgasket was replaced?
Your problems all sound like they are coming from air in the cooling system. I'm betting there is air in it and the system isn't full of coolant because it wasn't bled properly after the head was reinstalled.
This is best done with a coolant bleeding funnel which installs where the radiator cap goes, but can be done without it, only messier. With the radiator cap off start and run the engine until it's at full operating temperature. As it warms up you will see the coolant bubble, it will be unstable, and will spit some back out at you. When the thermostat opens the coolant level will drop, top it off and make sure the level stays consistent. once the level is consistent and no more bubbles are coming up then install the radiator cap and see if the problems are gone. You'll be in the area of hot coolant and steam throughout this, so be very careful.
You won't need to shut the engine off, and you don't want to shut the engine off until it's at full operating temperature and staying there, and no more bubbles are coming up.
At any time through this you can have the heat on to check and see if it's working. If it's not working with the engine hot then raise the RPM's a few times and this will help to force air out of the heater core and force coolant in.
It sounds like we're getting there though. If you look at the coolant temperature gauge it's staying steady now right, it's where it should be and not too hot, not too cold?
I never heard back from you after my last reply. We've got the air out of the system and were ready to move on.
Where does the temperature gauge stay now? Is it staying in the normal area, or is it cold?
I hadn't given up on you! I responded 1 minute and 36 seconds after you did last.
Our next step is to feel the heater hoses at the firewall, or the closest you can get. With the engine hot see if both hoses are hot, and note the difference in temperature between them. See if they are very close to the same temperature, or if one is noticeably colder than the other.
It's not a problem at all. Just let me know what you find and we'll go from there.