  Inspired by applications of gravity's rainbow in UV completion of general
relativity, we investigate charged topological black holes in gravity's rainbow
and show that depending on the values of different parameters, these solutions
may encounter with black hole solutions with two horizons, extreme black hole
(one horizon) or naked singularity (without horizon). First, we obtain black
hole solutions, calculate thermodynamical quantities of the system and check
the first law of thermodynamics. Then, we study the thermodynamical behavior of
the system including thermal stability and phase transitions. In addition, we
employ geometrical thermodynamics to probe phase transition points and limits
on having physical solutions. Finally, we obtain heat engines corresponding to
these black holes. The goal is to see how black holes' parameters such as
topological factor and rainbow functions would affect efficiency of the heat
engines.
