Avocados are best kept stored between 50-65 degrees Fahrenheit. They will just pretty much sit there, doing nothing, but will ripen over a long period of time, and it won't be even because of the weight being applied unevenly(they bottoms will ripen slightly first). Colder than that, and the seeds get weird, and the outermost part of the avocado gets damaged texturally, which can lead to rotting.
There are 3 ways an avocado can go: Ripening, Rotting, and Sprouting. They want to sprout, but you don't want them to. They ripen best between 65-72 degrees Fahrenheit(yeah its a tiny window. I kept them under a specific sink in the sushi bar because the temp was stable). You leave them wet or under pressure, or get them ripping hot, they will rot. This is never a good thing, it's the brownish spots you find that feel hollow when the fruit is still in it's skin. The stem can sink in to the skin and start molding. Above 72, they start acting like it's go time and breaking down. This would be a gradual, even process, but the avocado is losing heat on the outside much faster than the inside, so if you take a very cold avocado and put it on a warm counter for a day, you will get that dark green mush by the skin, and the stuff that's like an apple by the pit, and it will make a mess and annoy the crap out of you. This makes me want to try microwaving an avocado and getting it up to ~80 throughout and seeing what it does, might be on to something there. I don't have a microwave, so I'll have to file that one.
But all it takes is about 3 hours at 95+ degrees and the avocados will never be the same. If you take the firm green state, put them in an uncooled truck in Texas summer, and deliver them by putting them behind the vent to an ice machine, they will get those black specks you see at the grocery store. Sure they are firm today, but if you leave them on the counter, they will rot. If you cool them down and keep them humid, they will sprout, getting those stringy, woody lines in the meat that get stuck in your teeth.
If you get the avocado to *just* right before where you want it, and leave it on the counter for 8-18 hours, it will soften up considerably. If we took out perfect avocados for the bar at 10 AM and didn't use them all, the ones on the bottom were kinda crappy and soft by 11pm, so I'd put them in "use first" order.
A bright green avocado that feels as hard as a walnut, held at 68degrees, will be perfect for sushi in 4 days. The next day, perfect for eating out of hand or in salads, the day after that, guacamole. It is a happy day when you get the rock-hard ones, because they haven't been screwed with. I have learned, by handling unreasonable amounts of gator pears, to tell when the thing is hard in the center and soft outside, or when it has been treated badly and will turn out garbage...I grab them at the store and go to my Zen place and the Avocados speak to me....
Usually people want to see ripe produce at the store, but this is a lucky case for the modern global food machine. Avocados ripen *after* they fall off the tree, so they can be picked and shipped when they are as hard as olives, and ripen to perfection in your home.