  We analyze the consequences caused by an anomalous single-particle dispersion
relation suggested in several quantum-gravity models, upon the thermodynamics
of a Bose-Einstein condensate trapped in a generic 3-dimensional power-law
potential. We prove that the condensation temperature is shifted as a
consequence of such deformation and show that this fact could be used to
provide bounds on the deformation parameters. Additionally, we show that the
shift in the condensation temperature, described as a non-trivial function of
the number of particles and the trap parameters, could be used as a criterion
to analyze the effects caused by a deformed dispersion relation in weakly
interacting systems and also in finite size systems.
