  The Bronnikov model of nonlinear electrodynamics is investigated in general
relativity. The magnetic black hole is considered and we obtain a solution
giving corrections to the Reissner-Nordstr\"{o}m solution. In this model
spacetime at $r\rightarrow\infty$ becomes Minkowski's spacetime. We calculate
the magnetic mass of the black hole and the metric function. At some parameters
of the model there can be one, two or no horizons. The Hawking temperature and
the heat capacity of black holes are calculated. We show that a second-order
phase transition takes place and black holes are thermodynamically stable at
some range of parameters.
