i picked up some fairly ripe (firm but fragrant, definitely not overripe) peaches, apricots, and plums this weekend from the farmers market in Palo Alto. It was a pretty warm day and the fruits were in paper bags. When I got home, I put the fruits into the fridge, which was kept at 37 degrees. A few hours later, I went to eat one and found that all the fruits had basically turned to mush, so the skins were still intact, but the flesh was liquidy and I could squish it around.
I don't think the fruits miraculously overripened over the span of a few hours. I'm thinking it had something to do with the dramatic temp change going from warm outdoors to cold fridge. Potentially the humidity was too high as well in the fridge as there was condensation on all the fruits.
I thought I'd open the question up to those who know best. Please help me make sure this never happens again!