What bed clothing will help with my "broken thermostat"?

Dress the bed itself in layers. Cotton sheets, or a linen blend, if you can find it at a reasonable cost (hint: try http://www.overstock.com where you can sometimes find them at 75% off) - not synthetics. You need natural fabrics that breathe or you get trapped in a sweat bath when you start feeling too warm. The bottom sheet is the most important as you may find you prefer something other than a sheet directly over you.