+1 I had a nano tank (12 gallon) and the heater didn't turn on until October but ran off and on until February. This was in a house away from windows, however, I don't run my heat very often in the house. The small body of water changes temp really fast so the heater is def good insurance. Give it a 6-8 degree sudden drop in a couple of hours and consider your corals nuked.
Also, have you read up at all about cycling your tank? Did you buy live rock? Add any bacteria starter doses?
I think the main difference from starting a predator tank versus a coral tank is the cycling of the system. With the predator tank, its just fish. So, as long as your salinity and temperature are correct, you're solid. Then all you have to do is have the appropriate filtering devices in place to remove the biological load and add some water changes, and you're good to go.
With a coral system (particularly a nano) you have live rock and water changes as your main combatants against your biological load. Even if the live rock has already been cured and good to go, either way you would have to wait to finish your cycle before adding corals and fish, unless you dose some kind of bacteria head-start stuff (e.g. Dr. Tim's).
I may have missed that you've already cycled your tank (typically 1-3 months) but if you haven't yet, expect a cycle to be hitting you soon if you just set up your tank. You'll probably get a ammonia spike and higher levels of nitrites/nitrates and phosphates while your system is balancing out, which usually results in some type of algae growth or cyano. The conditions in your tank may be detrimental to the inhabitants of your tank which is why you usually leave the tank empty with just the liverock and sand until the cycle is complete.
The main reason I mention any of this is to prepare you in case you start noticing algal growth and your corals looking really ticked off.. then you may have an answer as to why. Also, seems like you're still shopping around for that perfect piece of liverock to be the centerpiece of your tank. When you add the new large piece of liverock to your system, it will cause another cycle in your tank. To avoid that, most people aim to have all their liverock in their system at the start and allow it all to cycle first, before putting anything in the tank.
These were the same stepping stones that I tripped on when I first started and wanted to share in case it helps. This hobby is such a rewarding one that I don't want anybody new starting out with a frustrating experience and be turned off by the whole thing. If you have any questions, ask away as you'll get some pretty good responses from the club. If you already know everything I said above, then ignore and maybe it'll help someone else who is reading your post. Good luck!
-Ty