It does get somewhat hot. As for how hot is OK, you may want to check with your Tesla local service people. It's never bothered me.
Also, remember that your battery can handle 80A and supercharging, but it'll live longer and age more gracefully if you charge more slowly. Also, lithium-ion batteries are happiest (and age best) when they spend as little time as possible either full or empty. If you use 50% of the battery on a day with lots of driving, for example, you may want to charge only to 80% so your use of the battery ranges from 30% when you come home to 80% the next morning.
Since I rarely needed more than 100 miles in a day, for example, I charged my Model S to 75%, giving me rated range of 195 miles. I'd come back home with 75-100 miles of rated range left in the very worst days (about 30% to 40%), and I've charge overnight at 20A/240V so it would take 5-6 hours to recharge back to 195. Lastly, every month or two, I'd do a full charge to 100% so the pack would "balance" itself.
I was never ever stressed for lack of range, and after four years my battery still held 98% of its original range. Anecdotal yes, but based on good science. Make sure you aren't living with range anxiety, there's no need for that. But while keeping enough range so you always have a great reserve, charging to a lower maximum will keep your battery healthier over time. You don't have to do any of this, but you have the choice if you want to baby your car and keep it in the best possible shape.