Hello joeh353!
I lurked for a while as well! Big time grats on setting the chew down. I used to smoke cigarettes, and I'm not going back as long as I can vape!
Regarding your nic strength: use whatever works for you to keep you from going back to the tobacco. I started out with 24 and 18, but within a couple of weeks I was using 12 mg/ml juice.
Regarding the heat issue: As I understand it, the strength of the nic doesn't play a big role in the heat you feel near the coil. I'd say "warm" is normal, "burn your finger" hot is not.
Two things do come to my mind though. First, do you know the resistance (ohms) of the coils you have in your tanks (often marked on them), and the voltage setting on your batteries? The twist batteries have an adjustment on the bottom to change the voltage from 3.2 volts up to 4.8 volts, if I recall correctly. Assuming your coil is about 2.0 ohms, your battery could be delivering from about 5 watts to maybe double that, depending on the setting on the battery. If you've got it turned all the way up, I'm not surprised it's getting warm. Have you experimented with how it vapes with your preferred juice at different voltage settings? If you're unsure of the resistance of your coils, and you don't have access to a good multimeter, most vape stores have a little box designed for just this purpose. If you want to own one of these boxes yourself, they run from ten to twenty dollars from a zillion online vendors. You'll want one if you decide to try rebuilding. I own good electronic test equipment, but I bought one of the boxes for the convenience.
Second, the juice being used might be thick enough that it's taking longer to wick up to the coil than you give it between draws. You mentioned you're a heavy vaper. Juices with a higher percentage of VG (glycerin) are thicker. If you've got a thick juice, and the first couple pulls on your device give good vapor, but after that you get a "burned" taste, this might be part of the problem. Airflow adjustments on your tank may have an impact on this. Experiment!
Plenty of reasonably priced devices will work with your existing tanks, provide larger battery capacity, and maybe act as a bit of a heat sink with their large metal bodies. Unless you want to jump up to really fancy devices in the $100-$200 range, I'd say see what you like in the $50 range. You'll need batteries and a charger as well. Plenty of choices, but I'd do some research, ask on the forum, before deciding what to buy and how many.
I'm sure that more experienced vapers will be along to give their thoughts, particularly those that own tank/battery combos identical to yours.
Safe travels!