How can I remove excess fat from stews or soups without refrigerating?
If you want to be really lazy about it, just get yourself a fat separator.  Pour in the soup, the fat will rise to the top, and you can do what you want with it (i.e. dump it).

If you're reading this in an emergency, you can do this with just a strainer.  You'll get better results if you chill the strainer before each skim, i.e. by rinsing it with very cold water.  The fat will tend to congeal on the cold strainer the same way it congeals when it's actually chilled.

I've also heard that the fat will cling to certain leafy vegetables, like lettuce.  If you have a lettuce head kicking around, try peeling off a leaf and dusting the top of the pan with it.