I
totally agree on the alarm... It should gong once the engine temp gets to 3/4 I think. It does gong once the coolant gets to a certain temp because mine did it, but by that time the engine is even hotter.
Anyway it could have been the water pump, best way to check is to run the car and just watch the temp guage. If it goes past 12o'clock then just shut it off. Check the upper and other radiator hoses to check coolant is flowing.
I'd probably change water pump/thermostat/coolant and maybe the fan clutch all in one go as its easy to do and not
too expensive for peice of mind. You've got the link above on how to do it. The guy who wrote that sounds like a pro.
Do a search for water pump - I've saw threads where the impeller's broken before so they will give you an indication of what you'll find when you ge the old one off.
Good luck mate, hope you get it sorted.