Radiator fan comes on when engine is cold causing cold heat inside the van(after installing new battery)

I have 2013 Chrysler van and still brand new under
48358mi, I been having this problems where in the Sumer
the ac/air won’t cool down and some time it dose with ac
fluid full. In the winter the temperature gauge of the van
stayed cold down to the second line if the gauge even
after hours of running. ( I got full coolant fluid).
I noticed the radiator fan runs when the engine is cold , I
unplugged the van while it’s running and I finally got heat
inside the van . But why the radiator fan runs on cold
engine causing cold heat inside the van after and before
installing a new battery ( when I first installed the new
battery it did work just perfect and I have good heat in the
van but after an hour it went back the same)+ ( the van
dose not stay running all the time but It runs as if the
engine were hot on cold engine )