Teachers in France are risking their own and students’ health in overheated schools as a severe heatwave sets new record temperatures, education unions said, urging staff to strike over “unacceptable working conditions”.

Several teaching unions on Thursday issued a joint statement denouncing a “blatant lack of preparation” by the government, after teachers have had to work in classrooms where temperatures reached up to 40C.

“The health of staff and pupils is being put at risk,” unions said, suggesting staff strike individually wherever and whenever they felt it necessary.

Most of France is under red alert, and the heatwave is expected to reach its peak on Thursday. Authorities closed 3,500 schools considered too dangerously hot and reduced hours at a further 10,000.

Most French school buildings – and their exposed playgrounds – were not designed for extreme temperatures. Many buildings are not properly insulated and most lack air-conditioning. Many schools were designed with large windows and no external shutters, causing classroom temperatures to soar above 30C or even 40C.

In some nursery and primary schools, teachers have had to keep curtains closed and spray children with water to try to cool them.

France is struggling to adapt its heat-trap school buildings for the exam season as hundreds of thousands of teenagers sit national tests in the heatwave.

The education minister, Édouard Geffray, said on Thursday that the “brevet” exams, which more than 850,000 15-year-olds begin sitting on Friday, would go ahead despite record temperatures.

Geffray said the exams would take place in the mornings and be over by midday. Desks would be spaced out to allow fewer students per room. Water would be handed out and rules adapted to allow students to take pauses and to leave their desk to cool down.

He told France 2 TV: “We’ll try to create optimal conditions – well, less unpleasant conditions – for the exams to be sat. But I think it’s better for students to do their exams now rather than not at all, or to postpone until September.”

In high schools, students have been taking their crucial baccalaureate oral exams throughout the heatwave, with some, as well as their examiners, feeling faint and even having to be treated by school nurses. Students have complained of being unable to revise in their homes, which are often heat traps.

The Île-de-France region, which includes Paris, has issued €1m (£860,000) of emergency funding to help high-school exam centres buy fans and cooling equipment.

In Paris, many parents decided it was safer for children to be at school than in overheated homes in record temperatures.

Geffray said not all schools would close completely because for the many French children living in heat-trap homes, a hot school might be preferable. “If it’s 40C in children’s homes, and 30C in schools, I prefer to adapt school activities for them,” he said.

Geffray said that from next summer all national exams would be held in the morning, rather than the afternoon. But unions have called for a complete overhaul of school buildings and exam scheduling to deal with heatwaves, which are hitting earlier in the school year.