  There are some examples in the literature, in which despite the fact that the
underlying theory or model does not impose a lower bound on the size of black
holes, the final temperature under Hawking evaporation is nevertheless finite
and nonzero. We show that under some loose conditions, the black hole is
necessarily an effective remnant, in the sense that its evaporation time is
infinite. That is, the final state that there is nonzero finite temperature
despite having no black hole remaining cannot be realized. We discuss the
limitations, subtleties, and the implications of this result, which is
reminiscent of the third law of black hole thermodynamics, but with the roles
of temperature and size interchanged. We therefore refer to our result as the
"complementary third law" for black hole thermodynamics.
