Perhaps that puts a bit of load on the engine, causing it to run slightly differently and that happens to resonate with some piece of sheetmetal somewhere. Sound travels.
Get a stethoscope and probe around. One of these will help you retain your sanity:
http://www.harborfreight.com/mechanics-stethoscope-41966.html
If it does end up being a heat shield, you can often fix it by putting a large band clamp around it. They are very often mounted with sheetmetal ears that just rot away.
They sell the larger band clamps at Lowes and Home Depot’s plumbing department:
http://www.pipe-clamps.com/productsimages/12mmbandclamp_164865.jpg
Edit: I see @PvtPublic already mentioned that as a possibility. I agree. Look at that first.