Stick-on thermometers are ok... but if your room (air) temp is signifigantly lower or higher than the tank (water) temp, you'll get wonky readings. In-tank thermometers, which are only affected by the water temp, are generally far more accurate.
Meat thermometers also work well for instant and accurate tank water readings. Just don't stick it in the fish! ;)
Oh I forgot, lol: once your ammonia & nitrites are @ 0ppm, and your Nitrates are in the 5-10ppm range, it will be safe to introduce fish. You'll want to float the fish (in their transport container) in the tank for a few minutes, to equalize water temperatures. Then, little by little, add the new tank water into the transport container, so the fish can adjust to the different chemical make-up of the new water. I'm cautious, and the water transitions can take a few hours.
Once the little buggers are in the tank, I let them get used to their new homes. If they look eager to eat (my bettas were!), I'll give them a tiny amount of food, and start the regular feedings 24 hours later.
My catfish needed two days to acclimate to their new tank before they wanted to eat... and then, only at night.
Woke up early today and tested the tank water. Ammonia and Nitrites were at 0ppm, while Nitrates were 0-5ppm.
Fed him, then took a bit of water from his 1 gallon and replaced it with water from the 10 gallon every 10-15 minutes. After that, poured him into the container with the mixed water and let him acclimate for about 30 minutes.
I came home from work and checked up on him and he's doing fine. I did put a piece of aquarium foam around his filter inlet to baffle it's intake force, since Airplane did seem flustered everytime he swam near it.
Your tank may be 'mini-cycling' now that your betta is actually in the tank, producing waste.
It is not unusual for 'mini-cycles' to occur. It can happen when adding new fish or anything else living into the tank, and somtimes after large water changes.
Do a 10% water change, and check the tank the next day. You want to make sure the ammonia and nitrites are kept as close to non-existant as possible.
Nitrates up to 20ppm are not a worry; at 40ppm you'll definitely need a water change.
Also, do not overfeed Airplane. A couple of pellets a day is all they need. Skipping a day now and then is ok too, especailly if they are looking bloated.
Overfeeding leads to fish illness and poor water quality.
Keep an eye on your chemistry through the mini-cycle. Once things are leveled out, with no big changes and water changes/gravel vacs, you should be able test once a week (sooner, however, if your betta seems distressed).
You might have mini-cycled when you put the betta in, and could be at the end of it. We'll see.
I wouldn't move your betta. Heck, the water in the tank is *perfect* now, lol!
I think you'll see the nitrates creep back up over time. They're living in your filter and elsewhere in the tank, doing their thing to convert waste. With the big water changes, they're diluted but they're there.
Check the tank in a week, and see where you are. PM me if you need to! :)