Your iPhone 13 Mini will get warm during processor intensive tasks . It may even get hot at times depending on ambient conditions and the level of processor demand applied. All this is normal. If your iPhone gets too hot to operate then it will shut down as a safety precaution. If it has not shut down then it is not overheating and operating / charging normally.
If your iPhone 13 Mini gets too hot to touch often then you can have it examined at the Apple Store or at an Authorized Service Center and take advantage of the 1YR Limited Warranty from Apple.
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