If they're not out of
rigor mortis ("stiffness of death"), they can be practically inedible unless cooked really, really, really slowly. Apparently if you can get them cooking before they go into rigor, you're ok - I really must try that sometime, now I can process a chook from whoa to go in about 10mins (rather than the 2 hours the first one took!!).
They go into rigor about 15-20mins after death. You can tell when the drumstick no longer moves easily in the hip. You now need to wait until that hip movement is smooth and soft again. This can be anywhere from 24 hours to 3 days, depending on the temperature they're sitting in.
I've run some (VERY) cautious experiments and am pretty confident in saying that the higher the resting temperature, the quicker they come of of rigor. So going in the fridge from immediately after processing or after defrosting, I find I need up to three days (so if I process on Sunday, I won't be eating until at least Wednesday). If I leave it overnight (say in the laundry, which stays relatively cool - let's say 14-16C overnight) and then refrigerate, I'm good to eat Tuesday.
If I were to leave it out for a whole day, it would probably be 24 hours. However, in the hot Australian climate, that's really risky, and I cannot recommend it.
We do have a wine fridge now, however, bought for curing meat (it's actually too hot for wine!). It keeps a nice regular 12C and is obviously fly-proof. I might try resting a chook at that temperature and see how long it takes.
Note - if we're not planning to eat a chook within a week of processing, we freeze as soon as they're cleaned and done. Frozen chook still needs to be rested, and of course you need to add defrosting time. I'm finding defrosting overnight in the laundry, then resting in the fridge, works fine. I managed to speed up the process by taking the bird out of the fridge on the second night and leaving overnight; we could have cooked it that evening, no problems.
The exception is when poaching or making stock. I put frozen birds directly into the stockpot and the resulting poached meat is fine for use in stir-fries, risottos, pasta sauces, etc. (Tonight's dinner being evidence

).