  We study the thermodynamic phase transition in the rainbow Schwarzschild
black hole where the metric depends on the energy of the test particle.
Identifying the black hole temperature with the energy from the modified
dispersion relation, we obtain the modified entropy and thermodynamic energy
along with the modified local temperature in the cavity to provide well defined
black hole states. It is found that apart from the conventional critical
temperature related to Hawking-Page phase transition there appears an
additional critical temperature which is of relevance to the existence of a
locally stable tiny black hole; however, the off-shell free energy tells us
that this black hole should eventually tunnel into the stable large black hole.
Finally, we discuss the reason why the temperature near the horizon is finite
in the rainbow black hole by employing the running gravitational coupling
constant, whereas it is divergent near the horizon in the ordinary
Schwarzschild black hole.
