Timing Belt Tensioner
The knocking/rapping sound is the same hot or cold. It was 40 degrees this morning when I started my car and it sounded the same after I drove ten miles. It does seem to go away upon acceleration, not as loud. It doesn't sound like valves out of adjustment, but I might check them as well as checking the belt to see if it's loose. I had thought another possibility would be alternator bearings, but its pretty loud for that.