A few points I'll add to anyone considering stage 2 on a '16+. I've found the Tundras to not have this issue, but the LC/LX do not like any injector other than stock or TRD green ones that come with the Magnuson kit. IIRC stock injectors are 372cc and the TRD's are 535cc. I'm 1 of about 4 other LC/LX that I know of in Colorado area that have a warm start issue with aftermarket injectors. Experienced tuner said Prospeed, Fuel Injector Clinic, and DW, all 650, 750, 775cc cause this. He just did a '21 HE with TRD's and no problem.
Getting a stage 1 tune essentially puts the 535cc injectors near max duty cycle. I have not heard of anyone using a larger injector and not have intermittent warm start issues....seems we are stuck at stage 1 for the time being.
Other mods that are easy to do to increase cooling for towing etc- even if you don't have a SC:
1. TRD radiator cap to increase the cooling system pressure over stock. 16psi to 19psi or something like that.
2. Swap to Toyota RED coolant over the pink extended interval. Changing every 25k may seem short, but every 100k is just lazy.