You will likely be annoyingly loud but otherwise fine. As always, you are liable for your own compliance with local noise ordinances.
I would recommend that you drive with the windows up until you give the car to the shop in order to avoid any risk of carbon monoxide poisoning. For example, don't drive with the trunk propped open: the low pressure behind the car will trap a bunch of exhaust back there and you don't want it coming into the car with you.
The risk is pretty low but you'll feel better if you're already concerned.
It's unlikely that the tank will notice any increase in temperature: it's used to being in the vicinity of hot metal carrying exhaust fumes. Now it's just going to experience the fumes directly.
When I replaced my muffler some years back, I started the car with the muffler off and was seriously tempted to drive around making a huge racket without any concern about exhaust fumes. My son convinced me that we'd get into too much trouble. He did agree that it sounded glorious, though....