I would say absolutely not!
I ran a Smart car (similer motor) for two summers in Cyprus and it didn't use any coolant at all. Cyprus summers are hot as well.
Check that you haven't got a tiny leak on any pipework that could be spraying coolant out when hot and up to pressure.
This type of leak cannot been seen when engine is cold and not pressurised, any coolant that has 'sprayed' will have evaporated leaving no sign when you look for it.
This happened on my Delica, a small pipe at the back of the engine had the tiniest of pin prick holes in it that only opened up when hot, under pressure.
Hope that helps. Good luck with it.