My car overheated after being in a idle position for 15 minutes is that normal?

I just bought this 2006 Chevy fit Equinox and I've had it for
about 2 months it was in the first week I noticed it would
when you weren't idling position with the air conditioner on
for more than two minutes the temperature gauge would
go up and up and up two almost three quarters of the way
and then once I started rolling again it would go back down
so every time I come to a stop light at the temperature
gauge to go up up up until I took off and then go back down
so I went and checked YouTube to find out what how to fix
it when the answer I got was that I needed to flush out the
radiator and put a new antifreeze in it half and half and
make sure I bleed all the air out of it cuz that's usually what
causes it to overheat is there's air in the system and also
change the oil in use synthetic high mileage synthetic oil
for the oil change so I did that too and I also replace the
thermostat so anyway I did that and it worked fine for about
3 or 4 days and then all of a sudden it started doing that
overheating again so what I did is I wouldn't bleed it it again
and I got all the air that I thought was out and then tighten
it back down and it worked fine for three or four more days
and then I had to bleed it again so finally I had to go to the
dealership because my temporary tags were going to
expire on July 13th so I went there on July 11th to find out
why it where my permanent plates are in a dealership says
that we forgot to do it missions I don't mean to do the
admissions before we can get the the new plates so they
wanted to take it down and do it and ice is why I need my
vehicle is there anyway you can give me the money and I
can go do it so they did and it was on a Friday and so I went
to do it and the check engine light came on as I was pulling
up into the emissions place so I wouldn't even going to try it
because I didn't think it would pass because of the check
engine light coming on so over the weekend just ran it as
usual and on Monday I was going to take it in to him and I
want Sunday I told mrs. Look this thing it's overheating bad
now I suppose I can't even go I have to go like a half a mile
at shoots all the way up I have to stop and let it cool down
open up the the cap the pressure cap to into the plastic I
guess you call that I don't know what you call that bull
plastic tank but that's where you put your antifreeze and
water and stuff so I waited it cool down so I can take it off
without a blown off and so I did that filled it back up and I
can go buy another two miles till I told him all that and they
should just drive it down here and we'll take care of it so I
got first thing in the morning I was able to drive it all the
way down there cuz they had sat out all night and Toes
completely cool so I dropped it off there and they said
they'd have it done in a couple days well first thing they
found out is the heater core had gone bad so they replace
the heater core and took it out and drove it and I guess
after driving it realized after head gasket had been blown to
so they told me they were going to have to fix that so that
added more days to it so they had it for like a week and a
half by me and gave it back to me and but they told me the
air conditioner doesn't work that they need to replace some
parts something to do with the where you turn the fan to
higher speeds there's something in there that's bad he says
you can turn the fan on but nothing but hot air comes out
and they don't know where to get the parts because of
vehicles what 14 years old so they're having problems
finding the parts for it so right now I've had it for about a
week and so tonight I parked in a parking spot to do
something on my phone while sitting in those about 20
minutes and I had the engine on and all of a sudden it
completely overheated again and so I turned it off and I
went and took some water and poured it on the radiator to
pull it down and I sat there for about an hour and then I
took off and came back and you know it was completely
normal all the way back to where I was staying at so I don't
know if that's normal for after all that being done for me to
sit at an idle position with the air conditioner doesn't work
for the air conditioner is not on for it to sit there and
overheat like that just sitting in idle for 15 minutes so I don't
know what to do with this point I'm going to have to tell the
dealership you know it's overheating again and I don't know
if I have a lemon law case or not but I've noticed that I've
read a lot of issues that the 2006 Equinox has a lot of
overheating issues and so I don't know what to do at this
point and I don't know if they're lying to me about the air
conditioning not working because of some control it to me
if it's the fan comes on the fan comes on how does that
have anything to do with why cold air isn't blowing up in my
opinion the only reason cold air wouldn't blow out as if it
needs Freon put in it or the air conditioning motor or
whatever system is completely boring and it needs a new
motor so if they're trying to tell me it's as to do with the
control of that turns the fan to high and low so I don't know
what to do at this point if someone can help me out