Why does my heating shield make noise

One or more fasteners are loose or missing. Another possibility is the heat shield is bent reducing the clearance require to prevent a rattle. this should be a quick and easy repair that will cost you less than $100. A third possibility is a broken exhaust hanger that allows the exhaust system to move far enough to contact the heat shield. One more possibility is a broken or wore out engine mount. If engine movement is excessive that may allow the exhaust to contact the heat shield.