2001 grand prix

Radiator fan(on passenger side). Won't turn on
unless I have defrost or A/C on as far as I can tell.
When I'm in stop and go driving. Will over heat
temp just keeps climbing to the point I will start
thinking about shutting car off for a bit. Once I
start driving it will start to drop and will get all the
way back to running temp... Seems to only do it on
the warmer days as spring time in Minnesota I get
hot days and cold days cold days it's fine hot days
it heats up.
1. Fan motors both work.
2. system bled.
3. Checked every fuse and rely twice.
So looking for where to go next starting with the
next most common issues and  cheapest as it is a
2001 not looking to break the bank. But also it has
the 3.8 so pretty much the only thing that will kill
the motor is over heating and seizing up.