Having had every pixel except the 4, 6, and 9, I'm gonna tell you that I had overheating issues on the pixel 1 and 2, and that battery life has been decent for me (a moderate phone user) on all of these devices except the pixel 3 which towards the end had the memory leak problem and was using battery when it wasn't supposed to be. Most of my overheating issues have happened when the phone is charging (mostly using wireless charging or charging in a place that's already got a high temp like in a car).
I'm not sure you're going to get the battery life you're looking for out of an older phone unless it's brand new/never been used or you degoogle it with a ROM like Graphene OS.