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It could possibly be that your heat shield which covers your exhaust pipe/catalytic converter has come loose. My 2000 Taurus SE began making a chirping noise right after I had hydroplaned out of control on the interstate during a heavy rain. I figured I had knocked my exhaust manifold loose or something worse, and come to find out, the right front corner of my heat shield had ripped loose where the bolt attached it to the underbody of the car. So the vibration of the car caused it to vibrate and created a squeeking/chirping sound. The thumping you described could be the shield hitting the underbody as you drive. I could be totally wrong, but your situation sounds similar to one I experienced. Hope I was of some assistance.
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