I can't speak for Madrid but here in Lisbon at roughly the same latitude we have no central heating and we usually go by with a single small ~900W space heater. According to wikipedia the all time record for low temperatures was -1°C, so it's usually fine.

If the temperature was to drop to below -10°C I'm not sure what I would do. I'd try to buy a better heater, but so would half the city so that might be a problem.

Madrid tends to have more extreme weather than here though, I suspect because the ocean offers us a certain thermal inertia.