My parents used to tell me that the manure and shavings pile would catch fire but I think that was just to keep me off of it. My friends and I would slide down it, spread it all over and make a huge mess. Yes, I like the smell of horse poop
So do I !
But mom wasn't foolin ya. They will catch fire.
There are two main advantages to the tires, or the bales.
First is is the ease of harvesting your potatoes.
The other is larger spuds. Even in the ground, you will get a much better yeild the looser the soil is. Sandy is good, but not so sandy that you lose nutrients. You want nice soft, almost "fluffy" compost.
This is also true of carrots, the softer the soil, the larger the carrots.
But just to clarify, it isn't the external temperature that causes combustion, it is the internal temp created by the cemechal reaction of the compost. Compost piles catch fire and smolder even in the dead of winter, and I have seen many hay barns catch on fire in late fall and early winter caused by putting the hay away when it is still damp after a rain.
One thing is for sure though, if the cows get out and find your bales, they're going to love all the little surprizes they find in the hay!!