  In this work, we investigate the thermodynamics of black $p$-branes (BB) in
the context of Gravity's Rainbow. We investigate this using rainbow functions
that have been motivated from loop quantum gravity and $\kappa$-Minkowski
noncommutative spacetime. Then for the sake of comparison, we examine a couple
of other rainbow functions that have also appeared in the literature. We show
that, for consistency, Gravity's Rainbow imposes a constraint on the minimum
mass of the BB, a constraint that we interpret here as implying the existence
of a black $p$-brane remnant. This interpretation is supported by the
computation of the black $p$-brane's heat capacity that shows that the latter
vanishes when the Schwarzschild radius takes on a value that is bigger than its
extremal limit. We found that the same conclusion is reached for the third
version of rainbow functions treated here but not with the second one for which
only standard black $p$-brane thermodynamics is recovered.
