  We study the phase transition of rainbow inspired higher dimensional
Schwarzschild black hole incorporating the effects of the generalized
uncertainty principle. First, we obtain the relation between the mass and
Hawking temperature of the rainbow inspired black hole taking into account the
effects of the modified dispersion relation and the generalized uncertainty
principle. The heat capacity is then computed from this relation which reveals
that there are remnants. The entropy of the black hole is next obtained in
$3+1$ and $4+1$-dimensions and is found to have logarithmic corrections only in
$3+1$-dimensions. We further investigate the local temperature, free energy and
stability of the black hole in an isothermal cavity. From the analysis of the
free energy, we find that there are two Hawking-Page type phase transitions in
$3+1$ and $4+1$-dimensions if we take into account the generalized uncertainty
principle. However, in the absence of the generalized uncertainty principle,
only one Hawking-Page type phase transition exists in spacetime dimensions
greater than four.
