  Thermodynamic stability of black holes, described by the R\'enyi formula as
equilibrium compatible entropy function, is investigated. It is shown that
within this approach, asymptotically flat, Schwarzschild black holes can be in
stable equilibrium with thermal radiation at a fixed temperature. This implies
that the canonical ensemble exists just like in anti-de Sitter space, and
nonextensive effects can stabilize the black holes in a very similar way as it
is done by the gravitational potential of an anti-de Sitter space. Furthermore,
it is also shown that a Hawking-Page-like black hole phase transition occurs at
a critical temperature which depends on the $q$-parameter of the R\'enyi
formula.
