No heat is not going to be an issue for you. You will not be able to pull 200 amps from your batteries for any meaningful amount of time for them to get hot enough to worry about. Using 1% rule on battery voltage sag, your batteries are only good for 20 amps (C/5) or 1/10th what you want.
Good luck, time for me to go play
Good luck, time for me to go play
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