ok, so can we confirm that you get a bleep? i think it bleeps 3 times for low coolant levels..!?
why when cold? well the coolant level will be lower the colder it is and possibly the electrical connector plugs get affected by the cold? ive had two leons, both have suffered from it even when the coolant was within the correct range. - both however worked fine when i ensured the coolant level was at the top end of the correct range. (when cold!) when the coolant is hot it will be above the top line due to expansion.
So i would ask is it at the top end of the correct range?
The next thing would be to take the expansion tank lid off, then wiggle and scrape the two metal prongs you can see in there from the sensor.
Then remove the sensor electrical connector plug, ensure all contacts are clean and give a good contact and then plug back in. (if you have any electrical conduction gel or something that may improve the contact then that would be good).
see how it goes,
if this doesnt
help then you can buy a new expansion tank.
(although im not aware of any change to the design and so in a year or two it may do the same).