Sounds like you want a continuous brew(CB) system. For a CB system you'll need a 2.5-5gal setup. Any more than 5gal and you can have problems with getting enough oxygen to the bacteria. I'm currently running a 3gal setup with a stainless steel spigot. I started with a 1gal kit and made a few batches, but it was moving too slowly for my desired consumption. So I bought a 3gal jar with a raised base and spigot so I could easily bottle from it. I made a 1gal batch (I have a total of 3 SCOBYs in there, my original mother and the two that formed through previous cycles) and let it go for two weeks to get it nice and strong, then I poured that into the 3gal and added 2gal of sweet tea to top that up. Once you get a CB system up and running it can take as little as 3-5 days to ferment newly added tea, because you've got over a gallon of starter and mature SCOBY in there. You can either drink it as you like straight from the jar or bottle up to 2/3. As for maintenance you can top up as you go, or wait until you get down below half-1/3 and then refill.
As for your temperature question, the SCOBY will not do well at 60*. Ideal conditions are between 75* and 85*. I keep my house pretty cold during the winter months, so I wrap a seeding mat around my jars to keep them at around 80*. They're fairly inexpensive and if you're going to go through the trouble of setting up a home brew system it's definitely worth the extra couple bucks.
