Basically, you can do like Tesla and go with LiCoNiAlO2 to get the highest possible energy density, at the cost of higher internal resistance (i.e. dumping lots of current produces lots of heat).
Or you can do like Formula-E cars (or RC helicopters, drones etc.) and go with LiFePO4 and sacrifice some range for the ability to dump massive amounts of current all the way to empty.
Cooling is fine and dandy, but it's hard to make efficient cooling reach into the internals of batteries. Reducing heat buildup pays greater dividends.
But putting it into perspective with some other great cars on the racetrack: the 2017 Honda Civic Type R is widely regarded as a bucket full of fun on a track, and would likely beat a Model S around the Nürburgring Nordschliefe even if the Model S didn't overheat; yet it "only" does 0-60 in 5.4 seconds.
And in general, 0-60 isn't useful at all on an actual race track because if you're spending time doing less than 60 mph, you're Doing It Wrong. Keep in mind the aerodynamics (spoilers, splitters, diffusers etc.) that make racecars actually work, only become effective once you're doing at least 80 mph, preferrably a lot more.
Take a look at Richard Hammond on the Top Gear episode where he gets to drive an actual F1 car to see what I mean. Mostly he spends his time not being able to go around corners because he's driving too slowly.