How many batteries can i put through my P3A during a day out , say i had eight could i run them in the drone one after another or would i need to give the drone a brake after x number of flights.

i would allow it to cool for 10 mins. or so after a couple of flights.

I've flown multiple batteries on 95+ degree days with no problems. If you are flying in cooler environments, I would not worry about it much.

I live where it gets up to 120 (hot) but I fly aroubd 100, really it depends how long you use the Camera & Gimbal, if you have the video on all the time it will get hot also if you fly 20 mins. I would give it a brake after each time you fly

Please let the aircraft cool down if the temperature gets up. I personally recommend to give it a brake after each time.

I've seen youtubes of guys whose motors burnt out from back to back flying without a break