Typically, one day will give you a fairly sour beer, and in two days it will be pretty tart. A good tip is to buy the bugs from White Labs or WYeast, and pitch them into the mash to make sure the right bugs get a foothold (who knows what else might be on the grain).
Try your best to keep in in the 120 range after the initial sach rest, an oven set to warm is the un-green method (running your over for two days straight), as long as it doesn't get too hot. A warm attic is another good option, especially for those still having summer heat. The right temp will allow the right bugs to do their work. I have heard some people say they fill the dead space with balloons or ping pong balls, to minimize O2 intake and heat loss, less air in the mash tun means less air to come into contact with the grain bed. Also, don't move it around or mess with it too much.
If there's anything you don't want after the mash is done, it will be on the top of the grain bed, so draw from underneath and leave the last little bit, and you should get just sour goodness.