I'm pretty sure the cheapest mirrors still manage 80% with good quality ones in the 95-99% and 99.999% achievable if you're prepared to get fancy. So I'd say they're pretty dang close to perfect. Definitely well down the asymptote.

I don't get what point you're trying to make... They reflect some radiation depending on quality. Regardless how close to perfect they get, the answer to the original question is - no, they don't break the "everything heats up" rule.