They do still have a heat lamp, it’s now raised pretty high and Saturday will ge turn off day. It’s in our garage so I’m not sure if temp in there. Our days have been unseasonably warm in the 70s right now, nights in mid 40s
I suggest you try putting a thermometer in various places and see what temperatures you're really working with. The chicks won't care if they are inside or out, if the temperature is the same or if it's a few degrees cooler.
I also suggest that you turn the heat lamp off in the daytime, starting right now. (The chicks may peep unhappily because it's different. If they settle down in half an hour, they're fine. If they are still peeping after half an hour, they may actually be needing the heat.)
You can plug it back in at night if you think they need it for the rest of the week.
Also, you can take the chicks outside for the daytime and bring them back in at night--that lets them get used to some of the outdoor temperatures.
The garage will have more stable temperature than outside, so letting the chicks sleep there for at least a few nights with no heat lamp is probably helpful before having them sleep outside permanently.
I think you will probably be able to move them all outside within a few weeks, even with the shelter being the doorless doghouse you mentioned, and then work on integrating all four young ones together into the big flock.