I don't think the cooler will be any sort of an issue.
I wouldn't take any crap about it either...it's not a performance part, as long as its installed correctly and I assume its Ford parts and not leaking so good luck connecting a longevity upgrade with an engine failure.
As long as you don't have any obvious parts and your tuner doesn't wipe your ignition count they will have no reason to look further.
Heard lots of stories about this supposed "deep scan" but I'm highly skeptical that it exists.
None of the techs I know have any knowledge of such a scan FYI, and the Mrs has never heard of such a thing either.
She's deals with warranty daily on the service side and has warranty experience on the admin side as well.
Good luck and keep us updated.