Your thermostat is probably not stuck open. Instead, probably the plastic housing that it is in has broken internally, allowing coolant to go around the thermostat. In any event, you want to at least replace the thermostat, then coolant outlet pipe, and the thermostat housing. It would be wise to also replace the engine fill cap and the pipe from the water pump to the coolant outlet pipe. I can get you full part numbers tonight, but here are the partials now.
Cap Assy - Radiator 3W4Z-8A511-AB
Connection - Water Outlet 3W4Z-8592-AA
Thermostat Assy 2W9Z-8575-AB
Seal 2W9Z-8590-AB
Tube - Water Inlet 3W4Z-8548-AD
Gasket 96JV-8255-CB (need two of these)
Gasket XW4Z-8255-CA
Ring - Rubber -W707299-S300
Tube Assy 2W93-9N499-AC
Personally, while I had the manifold off to replace the 9N499, I'd replace the throttle body heater hose that connects under there.
Hose Assy 3W4Z-9F814-AA
You may also want to order a couple of intake manifold gaskets.
2W9Z-9439-AA
I'm not sure about the size thing. What part of it are they measuring? All gen II V8s use the same size. I think that 54mm would be closest (of the two choices) to correct. Edit: Looking at Rockauto, the RT1163 (37mm) is the correct one.
Instructions on how to put the thermostat together:
http://deneau.info/ls/s6x~us~en~file=s6x33007.htm~gen~ref.htm
Edit: Now with full part numbers
