I am hearing a thumbing noise like a flat tire in the rear but no flat tire.

In my opinion, which is difficult to form without hearing the noise in question, i'd be looking at the condition of the brake rotors in the rear. There could be some hard spots and some high and low areas that could be dragging on the brake pads initially -- especially after sitting overnight and allowing some surface corrosion to form. Incidentally, this is more an annoyance than anything -- if this is actually what is happening. Not a safety concern. However, it's good to have your vehicle inspected to be sure. www.repairpal.com/repair-shops