After around 10 days I posted on this sub confirming that I'd be returning the phone. Because although the performance was great (it even plays Xbox cloud games perfectly), and it looks beautiful and has all the latest pixel features, the battery didn't even last a day and it was too hot to use.
After some comments advising that I keep it for another week or 2 and that I'd see the improvements, I decided to trust my fellow pixel fans and stick with it. And boy did it pay off, I'm currently writing to you all from London, 30 degrees Celsius (86 Fahrenheit), in a park right underneath the sun, and it is cool to the touch. It has been so for the past week or so, have had no issues whatsoever. Had some app updates which completely got rid of the overheating. And the battery...it has adapted to my usage perfectly, it now gives me nearly twice more the screen time as it did previously.
So tl:Dr > one month in, I'd highly recommend this phone