I just did a comparison of Battery temperature in my TiCu FWAA with a 3A and 10A battery. There was ZERO temperature difference between the batteries.
here is the test data:
Test 3A battery on turbo for 60 seconds
start 900 lumens (my meter)
finish 83 lumens
Battery temp start 25C (my IR thermometer)
Battery temp finish 32C
wait 20 minutes for host to cool down to ambient temp of 25C
Test 10A battery on turbo for 60 seconds
start 1100 lumens
finish 88 lumens
Battery temp start 25C
Battery temp finish 32C