Let me be clear: I fully expect your new battery to be dead in a few days, unless you drive the car every day - and it's not the nozzle heaters.

ANd while we talk about "stuff the manual just does not tell you", your button that turns on the rear window heating element turns on two OTHER heating elements.
Note that fuse 4 protects ONLY the mirrors, so if the back window gets warm but mirrors don't, check that fuse.