You can take it off without changing the pump, there are 3 11mm hex head bolts and the top housing should come off - these are by the Cambelt covers.
Be careful tho, a car I got parts off in the scrapyard sheared one of these bolts as they corrode against the aluminium casing they thread into.
No - be VERY VERY
careful undoing the thermostat bolts.
If you search the forum you'll see they're a frequent problem - the bolts are M7 by 55 mm or similar - very long & thin so when the thread seizes in the bottom housing it is exceedingly easy to snap a bolt. Which is then a ******* to fix.
If you must take the thermostat out now, try to get a little WD40/penetrating oil onto the bolts - but beware of spraying lube toward the timing belt casing. I'd leave it until you've made some other checks 1st.
My first step now if I were you would be to check the water level in the expansion tank before you start the engine.
If it's up to the mould line between the 2 halves of the tank, that'll do at the minute.
Regardless of the level of coolant, I'd crack the bleed nut on top of the thermostat by a bit (13mm spanner I think). If you've got enough coolant it will leak from the bleed nut. If not it won't
As Zulu Ferret suggests, squeeze the hoses - the 1 to the thermostat and since every thing's cold, the one from the bottom of the radiator - they should feel 'heavy' to squeeze. If they feel empty, there is air in the system, & it 'll help move the air to the top of the system.
Nip the bleed nut up & top the coolant up in the expansion tank to the mould line if necessary.
Put the cap on the expansion tank.
Start the engine & let it warm, keep an eye on the temperature & the level in the tank.
When the temp gauge gets to about 90, the thermostat should open & the radiator & top hose should get hot (may take a couple of mins).
If the top of the rad is cold still, check the bottom.
Also, the narrow hose from under the throttle to the expansion tank will start to flow - this will be visible running down the inside of the tank (blipping the throttle makes the stream move & so easier to see).
Regardless, stop the engine at this point
If the temperature is sensible (~100C) loosen the expansion tank cap off just enough that it hisses & releases the pressure.
Let the engine cool & check the level again when cool.
If you could see a flow from the small pipe in the tank, the pipe's OK.
If the top of the radiator stayed cold, but the bottom was hot, you've got a load of air in the system. Loosen the tank cap.
Crack open the bleed nut, squeeze & hold the top hose & close the bleed nut back up - the water level in the tank should drop a little.
If both are cold, the thermostat's probably not working. So as above, be very careful undoing the bolts.
I'm worried as the water bolied out of the tank when I tried to bleed it out. I don't want to damage the heads or gaskets.
If you took the cap off the tank while the engine was over heating, this is normal - the system is pressurised to prevent it boiling, so when you take the cap off, the pressure's released & the coolant boils.
Although the gaskets can be a problem, the V6 is pretty tough so you're probably OK.