These will gradually melt away after about a second while you stand on them, dropping you onto whatever lies below. The ice itself does no damage, but fall damage or any hazards below could kill the Spelunker.
You can climb on a side of Thin Ice as though it was a normal ledge. In that case, it won't melt.
The Giant Yeti's roar damages this kind of ice as well as dropping ice blocks.
Enemies and items may stand on the ice without causing it to melt.