[Lil bastard]

A waterpump failure is usually (but not always) progressive. It begins by having some weeping from the pump cover where the shaft extends to the pulley.

Another issue with the Boxster waterpump is disintegration of the plastic impeller inside the pump. This too is usually progressive and as the impeller degrades, so does the car's ability to run in a normal temp range.

From what you describe, it could also be several other things you'll need to rule out.

It could be a failed or failing 'T'stat.

It could also be the result of air in the system - if you lose coolant, especially a lot of coolant, you need to fill and bleed the system of any air. There is a procedure for doing this and also a cooling system bleed valve which lives under the cover plate through which the coolant tank neck and oil filler neck protrude. You pry this up and then lift the D-ring on the coolant bleed valve. Run, drive the car a few miles with the valve open, being careful to keep the coolant level up (bring along a jug of pre-mix). Then close the valve and top up keeping an eye on the temp for the next few days. If it spikes again, not all the air was purged on the first attempt, re-bleed the system again.

I'm sure your issue is one of more of these things. Good Luck!

Cheers!