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Should be here somewhere...
Doesn't appear to be any of those. Also, if memory serves, it was a prose short story, not a script for a stage play or teleplay.
I remember reading this story in school, too! It was in one of those anthologies you got for the whole year.
I tried searching using the concept and vague bits of dialogue I remembered, but came up with nothing. When they give the thermos to the alien, the alien asks how it knows what to keep warm and what to keep cold, and the boy responds that he doesn't know. I'm pretty sure one of the kids talks about keeping hot chocolate in the thermos, and the other talks about there still being ice cubes in it at lunch (when they pack it in the morning).
I still have one of my old English books from elementary school around here somewhere, but I'm pretty sure the alien-thermos story wasn't in that particular one, anyway. Dang it.
BUMPITY, BUMPITY, BUMP.
I remember this too, but I have no idea what it was . . .
^^^ The play I linked does mention hot chocolate and ice, but I can't find any signs of a short story form.
It was definitely a prose story, not a play. One may have been adapted from the other, no telling which was first without finding the short story version. I recall the version we read in school had illustrations, and the aliens were the classic "green men" variety.
BUMPITY, BUMP, BUMP.
Behold, Perry the Platypus! The BUMP-INATOR!!!!
Okay, I found one of my old story collections from elementary school. It's called "Emerald Forest: Treasury of Literature" and the publisher is Harcourt, Brace, and Company. I'm pretty sure the alien/thermos story was in a collection of stories from middle school, but it might be the same publisher, just a different collection for more advanced readers (I was in the same school corporation for all of childhood schooling). I'm trying to look up other collections by the same publisher and see if I can find tables of contents.
This is a long shot, but could Trophies: Distant Voyages: Grade 5
be the anthology you're thinking of? Some of the available versions seem to have been published from 2003 forwards but the first version I linked (which is the teacher edition) was from 2002.
I can't find a synopsis but the cover makes it look like it may involve space travel/aliens and it was from Harcourt Publishers. A review on this page mentions that it features illustrations, which you said your anthology did. If the cover looks familiar, there's a good chance it's what you read.
The story you've read is called "Close Encounter of a Weird Kind" by A. F. Bauman in a collection published under the name "Space and Science Fiction Plays for Young People" available here.
edit: minor correction
Edited by skewview AFK with issues, will return
There's a short story that features an alien who comes to Earth in search of a legendary device that can keep cold things cold and hot things hot. He is given a thermos by a group of middle school-aged children. While it is rather odd that a star-faring civilization could arise without this knowledge, if memory serves it was portrayed as a rite of passage of sorts for the alien's people. I have vague recollections of reading this back in middle / junior high school, so it had to be first published before 2003 at the latest.