A black hole with an event horizon that is thermally equal to its environment will not be in equilibrium.  A black hole with the mass of about the moon and in free space would have the same temperature as the CMB. If it absorbs a unit of energy its horizon increases in size and it become cooler.  This means it will preferentially grow.  If it emits a quantum of Hawking radiation it will becomes smaller and preferentially radiates more radiation.  So there is no equilibrium.  This is because the effective heat capacity of an event horizon is negative.  

There is no physically possible way to hold a black hole in an eternal state, except for one case.  This is a black hole in an anti de Sitter spacetime.  In this case the geodesic of the AdS are “repelling,” or equivalently any clock observed close to the boundary is seen to demark time at a faster rate.  So the BH will not crash into the boundary.  Also the Hawking radiation emitted by the BH will reach equilibrium with the AdS.  This is one reason researchers are so interested in AdS spacetimes.  

Around $10^{50}$ years from now there will be within regions bounded by cosmological horizons large galactic BHs.  The temperature of the horizon by Hawking-Gibbon radiation will be lower than the horizon temperature.  As a result these BHs will quantum radiate away so that around $10^{100}$ years into the future they evaporate away in a final flash of radiation.