No. They only survive in tropical/subtropical regions.
A concerted effort to treat cases and reduce habitat can prevent it, too. The US wiped it out in the 50s; new cases largely come from travel.
USA wiped out malaria in the 50s using DDT which also made the California condor go extinct in the wild. During the 70s-90s DDT became illegal to use in most countries around the globe.
I’m not sure the USA would have been successful eradicating malaria without using DDT or something similar.
DDT caused the Bald Eagle population to drop from about 400,000 birds to just 47 nesting pairs.
No. Malaria epidemics occurred in medieval Europe, both in warmer countries (Italy, Greece) and in France, Germany and England. It was also common in portions of the US until large-scale eradication efforts.
It's unlikely to become a problem again because the climate is not optimal and these countries are wealthy, have advanced healthcare systems, and can spray everything with DDT again if they feel like doing it.
There were malaria epidemics in even quite temperate parts of Europe up to the mid 20th century, including Bavaria and even England, and it was endemic to parts of Italy and Greece. P. falciparum was found in bone samples of the Medicis.
Sadly, maybe wait 5 to 10 decades then it could exist in many areas were it does not now.
Malaria was endemic in Finland until the beginning of the 20th century, the people used to lived inside smoke-heated chimneyless log cabins together with animals, mosquitoes... and Plasmodium vivax...