Warnings have been issued in more than 40 provinces in Spain, with a red alert for the southern city of Cordoba.
Neighbouring Portugal has also placed four regions on an orange alert, the second highest level possible.
Both countries have warned that the searing heat will substantially increase the risk of forest fires.
Nearly all of Spain faced an "extreme" or high risk of forest fires on Monday.
"These are not usual meteorological phenomena," said a spokesperson of the country's national weather office, as quoted by the AFP news agency.
They warned that the exceptional temperatures posed "a very high level of risk for the population".
The Spanish cities of Cordoba, Seville and Toledo were some of the worst affected on Monday. Temperatures were expected to reach up to 44C in some areas.
In Seville, some people jumped off bridge to swim in the city's Guadalquivir river to try and escape the heat, according to AFP.
Spain's Guardia Civil urged people to drink at least three litres (five pints) of water a day and to avoid eating hot meals.
The heatwave is expected to spread, prompting concern in France and in the UK.
In 2003, a heatwave led to 70,000 more deaths than usual across Europe.
"I don't think this heatwave will have the same consequences as the one in 2003 because we weren't as prepared at that time," said French Ecology Minister Segolene Royal.
The high temperatures are expected to last at least until the end of the week.
The body's normal core temperature is 37-38C.
If it heats up to 39-40C, the brain tells the muscles to slow down and fatigue sets in. At 40-41C heat exhaustion is likely - and above 41C the body starts to shut down.
Chemical processes start to be affected, the cells inside the body deteriorate and there is a risk of multiple organ failure.
The body cannot even sweat at this point because blood flow to the skin stops, making it feel cold and clammy.
Heatstroke - which can occur at any temperature over 40C - requires professional medical help and if not treated immediately, chances of survival can be slim.
There are a number of things people can do to help themselves. These include:
What happens to the body in extreme heat?
Eight low-tech ways to keep cool in a heatwave
A heatwave in Spain and Portugal has triggered alerts across the region, with temperatures soaring above 40C and warnings of risks to residents' health.