You don't know what the fuck you're talking about.

Active cooling means practically nothing at those temperatures,

What temperatures? The 71°C of the pavement? As I said, there's air and physical barriers that keep that temperature from reaching the battery.

any cooling system is just a heat transfer device, that also generates heat itself. It just moves the heat elsewhere.

Yeah. That's the whole point. It moves the heat from the battery to the outside air, keeping the battery from reaching that 70°C number you're worried about. Which, while I'm at it, is a change from the earlier 40°C number you claimed is a problem.

So sure, it'll help cool the battery, but what power it takes for the battery to cool itself comes from the battery itself, thereby heating it up even more as it fights to cool itself.

Are you fucking serious? Think for a moment. Do you really think that the cooling system, by drawing power from the battery, heats the battery up more than it cools it? That's ridiculous.

Depends on the type of cooling, but even the less efficient cooling systems will be using a tiny fraction of the battery output, like less than 1% for most. Passively cooled batteries are going to have problems for sure but even then I'm not convinced there would be enough heat transfer for long enough from a 70 degree road surface to actually be a serious problem. The road itself would be cooling and unless you're just sitting over it for a long time it's not likely to become a real problem. A somewhat pessimistic (for volume, not for actual capacity) estimate would be 300kg of battery mass for 100kwh. Assuming middle range lithium ion thermal capacity that's about 300kj per degree k. So for maths convenience let's assume the car is 10m^2 on the underside and that's all in contact with the battery, going by the previous estimates (again, worst case for battery overhead purposes) and assuming the air is moving and already preheated to 70 degrees c it would take around 5 minutes to heat the whole battery to 70. Thanks for the maths problem though, was interesting to look into this stuff, I've made some big assumptions but it's looking very unlikely you're realistically going to have big issues with overheating unless you spend an inordinate time with an EV sitting over hot asphalt, I didn't consider radiative heat transfer but I wouldn't think that would make a huge difference given the albedo of asphalt also the ambient air would probably help cool more than I considered. It would be neat if someone with more knowledge on the equations has input though.