  Considering corrections produced by modified dispersion relations on the
equation of state parameter of radiation, we study the induced black hole
metric inspired by Kiselev's ansatz, thus defining a deformed
Reissner-Nordstr\"{o}m metric. In particular, we consider thermodynamic
properties of such a black hole from the combined viewpoints of the modified
equation of state parameter and the phenomenological approach to the quantum
gravity problem called rainbow gravity.
