if the ice box system is set up by someone who knows what they are doing, then the are sick! I can run a completely sealed room ice boxes take care of all heat!
Be sure if you take a portable a/c to get the one with 2 exit (one to push fresh air in) and (one to push hot air out) otherwise you will need to add some fitting to you re OUT. otherwise heat will be a problem because they push lot of HOT air. (Using one at the moment)