Firstly, I think you are mistaken about heat. It is objectively true that cities are hotter places to live in general, disregarding climate change. This is partly due to the large amount of materials which absorb heat from the sun, such as black asphalt in massive parking lots. It makes cities less pleasant, for sure.
I also don’t think you understand the “war on driving”… the point is that you have less freedom in a car dependent world. You can’t conveniently choose to walk to the grocery store a few blocks away when there are 6 lane roads which pay no respect to pedestrians. You can’t choose to take a train to a concert, since passenger trains are rarer and rarer.
You have fewer choices and less freedom if the only convenient choice is a car. And what if you don’t have or can’t get a car? Your mobility is extremely limited.
The “war on driving” is all about creating more choices and freedom for transit. It’s not saying all cars should be outlawed. It’s saying that the bus or train should be just as convenient as driving in a city, and that biking and cycling within a mile or two of home should be even more convenient than driving.
And, most importantly for you, in a city where everyone has many transit choices, driving is much more pleasant. With fewer people driving cars for trips that don’t really need them, there will be less traffic and less need for massive roads which are dangerous even for drivers. This video is very illuminating: https://youtu.be/d8RRE2rDw4k
In fact, I’d recommend watching even more videos on that channel to really understand why having more alternatives to cars is a good thing.