Car and train traffic also disrupted due to fire near Palermo’s airport as trees fall and buildings damaged in Milan.
The airport in the Sicilian capital was shut for several hours until 11am (09:00 GMT) on Tuesday as firefighters were putting out a blaze nearby that also disrupted road and rail traffic.
The incident added to Sicily’s travel misery at the peak of the tourist season.
The island’s main airport of Catania, Italy’s fifth biggest, was closed last week due to a fire in a terminal building and has reopened only for a few flights.
A heatwave has hit Southern Europe with scorching temperatures bringing increased risk of fires and deaths.
In some parts of eastern Sicily, temperatures rose to 47.6 degrees Celsius (117.7 degrees Fahrenheit) on Monday, close to a record European high of 48.8C (119.8F) recorded on the island two years ago.
On Tuesday, Italy put 16 cities on red alert because of the high temperatures.
They included Palermo and Catania, where power and water supply cuts that local officials blamed in part on the heat have been frequent in recent days.
In the north, an overnight storm in Milan tore off roofs and uprooted trees, blocking roads and disrupting transportation in Italy’s financial capital.
Transport authorities reported serious damage to the city’s electricity network while the Agence France-Presse news agency reported that water in the historic centre was temporarily shut off.
A woman was killed on Monday in the northern province of Monza when she was crushed by a falling tree.
On Tuesday, a 16-year-old girl at a scout camp was killed near the city of Brescia when a tree fell on her tent, according to Italian news agencies.
Firefighters evacuated the other members of the camp, taking them to a sports hall nearby, the ANSA news agency said.
On Monday, a Delta flight that had taken off from Milan’s Malpensa airport and was headed to New York was seriously damaged by a hailstorm and was forced to land in Rome.
Italy is one of the European countries most affected by climate change and suffered deadly floods in May.