2004 Chevy venture engine overheating in cold

So my friend has a 2004 Chevy Venture that is having trouble in the cold and is causing the engine to overheat. She added new coolant this morning but it wasn’t super helpful. After talking with me she turned off her car for a few minutes and when she turned it back on the heat gauge was about in the middle when measured. She was able to take it for a short drive to get to work (she was already running late due to this) and while she was driving the temperature gauge went down to where it normally is but when she stopped the temperature began to rise again.
I’m trying to help her troubleshoot her car as I have more car knowledge than she does but I’m not physically located near her and she wasn’t sure who to ask. This only happens when the temperature drops below freezing.
I’m wondering if anyone has any suggestions of things that she can try to look at before bringing it to her mechanic or if there might be any important things to mention to the mechanic.
Based on my prior knowledge and some googling I’m wondering if the radiator cap is rusted, the coolant hoses might have a blockage, or a gasket might need to be replaced. Without being able to get a good look myself it’s difficult to figure out and was wondering if anyone here has any insight.

Thank you in advance for any answers!!!

Is she adding a 50/50 mix of water and antifreeze?

Tester

Yes she is, that was one of the things I checked with her about, sorry for not including that information.

That’s where the heat gauge should read at operating temperature.

Tester

Ok, that’s what I was thinking but before that, when she had initially turned it on it was all the way up in the red. I think it got figured out but I just want to make sure that there isn’t anything else we should be aware of or do to try to prevent this from happening again!

Thank you so much

I would first check to see if the radiator stays/is full, and if that’s good, make sure the cooling fan is coming on. Especially when she stops and engine starts to overheat, if the fan (cooling near radiator) isn’t coming on, replace. Also, if it does come on, make sure it is spinning at a high revolution. I’ve had them spin to slow, it would be obvious if that was the case.
If the fan is good, you could try replacing the thermostat too.

Where is car be driven? LA? Toronto?
Jan is more/less cold in different places.