Why would milk form a dense emulsion when warmed?

About a week ago, I noticed that the milk I had bought a few days before seemed to curdle in coffee -- if you haven't done this before, it can happen with sour milk, and separates into tiny cheese like curds which end up in the bottom of the mug.

However, the milk was (and still is) not at all sour; the bags (milk is often sold in bags in Canada) are stamped January 3rd, and I've been drinking it all week (and using it my coffee and leaving the sludge at the bottom).

So today on a hunch, I took a bit of milk, put it in a rounded glass, and left this to sit warming on top of a mug of fresh java. Low and behold, a few minutes later it had solidified into something indistinguishable from smooth yogurt. Note the coffee was hot initially but not undrinkably so; there was no evaporation and the volume of the milk has not changed.

It actually tastes quite pleasant, exactly like warmed milk. But it has the texture of yogurt. The milk is either 1 or 2% (I threw away the outer bag) and was probably subjected to a microfiltration process called "trutaste", which I sometimes buy (the long Jan 3 shelf life is indicative of that).