Sometimes, though not often, a piece of asphalt, even a pebble or small rock, can be thrown up from the road surface and land on the pad where the pad rests in the caliper causing the pad to ride against the rotor. This causes the pad to build up heat and thus squeal. The hotter the pad the more the asphalt, in particular, "welds" itself to the pad/caliper. Check to see that there are no pieces of asphalt lying on the pads where they meet their mating surfaces with the calipers. I actually had this happen several years ago and had it "bug" me for quite some time until I discovered it when noticing that one of the pads had worn much more than the other. This uneven wear can also indicate a sticking caliper piston as mentioned in one of the other responses given to your problem.
