You do not need to notify Walmart. Some of them don't allow overnight parking, but they are typically ones that are not open 24 hours or are in/near cities.
You'll almost always see a few other trucks or RVs parking there overnight. I park where ever there aren't other people and away from the store, so I don't get parked in come morning time or have people anywhere near me.
We stayed in Florence, SC at the WalMart both ways on our trip from MD to FL and back. It was about 90 during the day and in the low 70s at night. We opened the windows and turned on the Fantastic Fan. I also had a regular fan plugged in to an inverter pointed on us in bed. Both nights we actually woke up a bit chilly before it started to warm up around 8-9am. I don't have a generator, but I'm sure you could use one. I'd just make sure it's locked up well to the frame or something. I usually find a spot under a tree and/or try to position myself so my bedroom side isn't facing the sun come morning time, which affords some extra sleep time.