I'm using 35 mm tires on my touring bike with 28/38 Specialized tubes. I've had three flats in quick succession, all in about the same place and each a very small hole, so small that it takes overnight for the tire to flat and you have to put it underwater to find the leak.
I've examined the tire and rim around where the flat occurs with a magnifying glass, washed and dried the inside of the tire with a towel, and rewrapped the rim with new tape. I can't find any thing that would have caused these flats. I've used the rim for more than a year with 28 mm tires without a problem.
I was inflating the tires to 80 instead of 60, the recommended pressure. Could that be the cause? I inflated to 60 for today's ride and so far so good but one day does not a test make. Besides, there could be a small hole in it now but I still wouldn't know till tomorrow morning.
I'm guessing you don't index your tire? If you line up the hot patch with the valve stem, you'll know where to check the tire for debris. I've had a customer come in with 3 flats in the same tube. He checked it 3 times, I checked it in the store once, inside and out. While he selected a new tire, I half-absently mindedly went over it again. Sure enough, there was a tiny sliver of glass in one of the cracks of the tire. It had a happy life in there. He would inflate the tire, and let it sit overnight. The next day, when he would ride it, the pressure of his weight was enough to force the happy little piece of glass into the tube. Remove the pressure, and it went back into hiding in the rubber. There are 3 lessons to be learned here.
Cervelo SLC-SL, Guru Photon, Waterford, Specialized CX
You've got some pretty thick tread there. There's a good chance you still have a little sliver of glass or metal shaving caught in the rubber. It works itself to the tube through the pressure of riding.
I would try once more to find the object. Turn the tire inside out and slowly go through and twist and bend until you find it. If you come up empty, buy a new tire.