We also call them potholders ...or, as my mom calls them, "countertop savers." Also 'hot pad' works. :)
I think the correct name is trivet, though. I always picture a fancy shmancy potholder though when I think of a trivet. Like, a mosaic tile that is some serious hardware.
We have some basket-weave like ones at my place, which I would feel strange calling trivets.
"Any reviewer who expresses rage and loathing for a novel is preposterous. He or she is like a person who has put on full armor and attacked a hot fudge sundae."Kurt Vonnegut