Is the Wave Function of a Super Cold Gas Different than at Higher Temperatures?

[Question Man]

Consider a super cold gas tube (of, say, hydrogen), is the wave function of the gas different than at a higher temperature? How about for a lone electron within the gas?

 

[dlgoff]

A Bose–Einstein condensate (BEC) is a state of matter of a dilute gas of weakly interacting bosons confined in an external potential and cooled to temperatures very near absolute zero (0 K or −273.15 °C[1]). Under such conditions, a large fraction of the bosons occupy the lowest quantum state of the external potential, at which point quantum effects become apparent on a macroscopic scale.

http://en.wikipedia.org/wiki/Bose_einstein_condensate"