  A Hayward black hole and magnetically charged black hole based on rational
nonlinear electrodynamics with the Lagrangian ${\cal L} = -{\cal
F}/(1+2\beta{\cal F})$ (${\cal F}$ is a field invariant) are considered. It was
shown that the metric function in both models possesses a de Sitter core
without singularities as $r\rightarrow 0$. The behavior of the Hawking
temperature and the heat capacity in these models are similar. The phase
transitions take place when the Hawking temperature has a maximum, and black
holes are thermodynamically stable at some event horizon radii when the heat
capacity is positive. We show that the source of gravity in the Hayward model
is questionable.
